"A delay is a form of retrograde (...) in which a force under pressure trades space for time by slowing down the enemy’s momentum and inflicting maximum damage on the enemy without, in principle, becoming decisively engaged (...). The delay is one of the most demanding of all ground combat operations. A delay wears down the enemy so that friendly forces can regain the initiative through offensive action, buy time to establish an effective defense, or determine enemy intentions as part of a security operation. Normally in a delay, inflicting casualties on the enemy is secondary to gaining time. For example, a flank security force conducts a delay operation to provide time for the protected force to establish a viable defense along its threatened flank. Except when directed to prevent enemy penetration of a phase line (...) for a specific duration, a force conducting a delay normally does not become decisively engaged."
FM 3-90 (chapter 11-5)
I'll spare everyone the nitpicking about that definition. My short(er) definition is as follows:
"A delaying action serves the purpose to slow down the advance of opposing ground forces by yielding ground for time. It is preferable for the defending force to not get fixed or engaged decisively. Slowing down the opposing forces typically is prioritised over reducing them."
I personally consider delaying actions as the dominant part of modern mobile warfare. Forces would be thinly distributed in most areas of a theatre of war due to a low ratio between forces and area, so "economy of force" is most important in most places. Save for harassment a delaying action can be executed with the worst ratio of friendly to opposing forces if only the friendly forces are technically no less mobile than the attacking opposing forces. This typically poor ratio of forces is what makes a delaying action "demanding" according to the U.S.Army definition above.
Befitting von Clausewitz' Schwerpunkt concept, you need to minimise defences in most places in order to amass enough or as many as possible forces for the Schwerpunkt or the main effort for decisive offensive action. Those reserves freed from failing in 'defending everywhere' could also have a "fleet in being" effect of deterring major hostile offensive operations by being available for counterstrokes.
Now about the textbook version of delaying actions (aggregated from many sources, not only the FM 3-90):
You divide the share of friendly forces that are suitable (speed, morale, training, equipment, supply state) into at least two different elements.
Engineers reduce the trafficability of the routes (blowing up bridges, cratering roads at bottlenecks, flooding terrain, causing forest fires to make forest roads impassable, fake and real mines, removal or manipulation of road signs etc.).
The element more close to the advancing opposing forces tries to force them off the road with long-range artillery fires (to slow their movement), and then forces them to deploy into battle formation (slower than march column) with a far ambush. A prioritisation of slowing down instead of attrition would typically suggest that this friendly force makes its presence known before the far ambush in order to force the opposing force to deploy and thus spend time without substantial line of sight combat (Remember? No decisive engagement!). A greater emphasis on attrition and an effort to build up a reputation for dangerous far ambushes early on would require to execute the far ambush for real. The problem is then to avoid decisive action even through the opposing force can move at 50+ kph on the battlefield and line of sight are often only 500-3,000 m and can be reduced further by obscuration efforts (mostly artillery-delivered multispectral smoke).
The defenders risk being overrun by a rapid counter-ambush assault. Obstacles (such as scatterable mines) may help in this regard.
A frontal far ambush makes withdrawal of the ambushers less difficult and an attempted flank attack on it costs the attacker more time, while a flanking far ambush allows for a better attrition effect, particularly the destruction of other than lead elements (such as bridgelaying and minesweeping tanks, which in the end may have a greater slowing effect).
So the defenders force the attackers to deploy, waste time in a minefield or unsuccessful flanking move and ideally withdraw in time to avoid decisive (close) combat, though possibly causing and suffering some attrition.
This forward delaying element then withdraws, and an incompetent delaying action would demand this very same force to set up the next far ambush itself. A competent commander would instead have arrangements for a second element to allow the retreating friendly forces to pass and execute the next far ambush. It's impossible for a single element to maintain a delaying effort without vastly superior mobility.
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Now about the modern picture:
(1) The advancing opposing forces are nowadays an all-offroad capable, all-motorised force. This is true even of Toyota technical-based improvised civil war forces in developing countries.
They can move in dispersion, with individual platoons or companies moving with several kilometres spacing. The delaying effort could then be the sum of (small) unit engagements. Attrition would naturally become more prevalent (since every far ambush salvo might eradicate an entire manoeuvre element) and frontal assaults (overrun attempts) on far ambush positions less likely. Flanking on the other hand would be more easily against the defenders, since inevitably some advancing manoeuvre elements will be farther forward than others.
(2) There's likely no front-line going to be established soon for want of enough forces, thus it's not so risky to be "behind" opposing forces any more. No front-line will cut such forces off any time soon, after all.
This allows for an alternative and supplement to the far ambush, especially on the operational (~corps command) level of war: Substantial forces* "left behind" or manoeuvring into positions behind an advancing hostile force would threaten its supply lines and its support elements (which are only marginally capable of line of sight combat). This would at the very least force a 360° security effort on the advancing opposing force, turning it into a moving pocket. This means a weakened tip of the spear and thus less offensive power (making delay by far ambush easier and attrition more important), but it's also most uncomfortable for the opposing commander. He might be tempted to 'clean up' those elements in his rear, which of course would cost a lot of time, since those elements can resist removal by a delaying effort of their own. A delaying effort in the 21st century does thus not need to be about withdrawal (the attacking opposing force may well move away from the bulk of friendly (our) forces when engaging a pesky element in its rear). Accordingly, it also doesn't need to be about trading space for time. In fact, space may be gained if the opposing force attempts to get rid of an element in its rear.
(3) Delaying actions may be considered to be shaping operations.
To slow an opposing force down allows for less-impeded friendly elements to manoeuvre into position for a decisive engagement (for a synchronised pincer attack, for example). To force a 360° security effort on the opposing force may reduce the surprise effect on such an action, but also reduce the opposing force's ability to resist it. A delaying action may also be used to slow down a withdrawal (another reason why a delaying action isn't necessarily trading away territory) in order to make a pursuit more effective.
Delaying actions may also be kept the dominant choice of course for days in order to build up forces or to exploit superior long-range artillery firepower or superior air/ground attack strength. Entire army corps might refuse to offer battle brigades vs. brigades if this improves their odds of success.** Tactics treaties are often excessively focused on how to win a battle during the battle, while the preferable course of action is to refuse battle until shaping operations almost guaranteed success in battle. This necessitates some alternative effect (other than battle or front-lines) to keep the opposing forces from advancing and accomplishing their objectives in the meantime.
(4) Delaying actions should refuse decisive actions, that is the delaying elements should avoid their own destruction. That's generally a good idea, but as mentioned before, the ratio of forces is usually disadvantageous in a delay, so offering battle to the death (of either the friendly or the hostile element) is typically a losing proposition in a delaying action. The problem nowadays is that about 80-90% of casualties are caused by indirect fires (non-line of sight combat) in conventional warfare, so the classic view that the delaying element would risk its destruction primarily in close line-of-sight combat is probably inaccurate and obsolete. Sure, close combat may still eliminate the element and make its withdrawal very, very difficult. Yet its destruction (or attrition high enough to make the element incapable of staying on its mission) is more likely by repeated artillery (and other support) fires. The focus for survivability on a delaying action mission should thus not be on avoiding close combat any more. Instead, it's important to avoid artillery and other support fires. Short range air defences, withdrawal within 2-3 minutes after giving away one's position, irregular movements to avoid shelling on the move between ambush positions and so on will require additional capabilities and efforts and narrow down the freedom of action of the delaying forces.
On the other hand, the destructive and inhibiting effects of indirect fires may be used to greater effect than ever before in the delaying effort itself. Modern artillery typically has about 30 km range, about 40 km with fewer munitions and 80-100 km range with very few munitions. A moving opposing force could be threatened by artillery almost at all times, potentially forcing it into a dispersed and offroad movement instead of a quick and efficient road march even without classic delaying actions (far ambushes).
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I insist that delaying actions are very, very important in modern conventional (state vs. state) mobile warfare. Meanwhile, field manuals still appear to imply that it's a poor man's choice and to be avoided if possible. Instead, I would consider it as the first choice, in preparation for (possibly never happening) brigade-on-brigade battles later on.
*: More than long-range scouts / LRRP / Fernspäher and in this case no Jagdkommando, for I emphasise mobile warfare and thus mounted combat in this text. I'm rather thinking of quite combat-capable armoured recce units.
**: I really need to write about the 'fleet in being' effect sometime..