on each other / one after another
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each other
Expresses a reciprocal or mutual relationship or action between two or more people or things.
Die beiden Teams treffen morgen zum ersten Mal aufeinander.
The two teams will meet each other for the first time tomorrow.
on top of each other
Describes a position in which one thing lies on another; stacked.
Bitte lege die Bücher ordentlich aufeinander.
Please put the books neatly on top of each other.
one after another
Describes a sequence in time in which one event happens directly after another.
Die Besprechungen folgen heute Schlag auf Schlag aufeinander.
The meetings are following one after another in quick succession today.
with each other
Used with verbs or adjectives to describe a mutual emotion or reaction (e.g., wütend aufeinander sein, aufeinander hören).
Nach dem Streit waren sie eine Woche lang böse aufeinander.
After the argument, they were angry with each other for a week.
'Aufeinander' (on each other / one after another) is an adverb made up of the preposition 'auf' (on) and the reciprocal pronoun 'einander' (each other). It literally means 'auf einander' (on one another) or 'on each other'.
Die Kinder kletterten aufeinander, um die Mauer zu überwinden.
The children climbed on top of each other to get over the wall.
'Aufeinander' (on each other / one after another) is often combined with verbs that normally require the preposition 'auf' in order to express a mutual action. For example, 'warten auf' (to wait for) becomes the phrase 'aufeinander warten' (to wait for each other).
Wir haben eine Stunde lang aufeinander gewartet.
We waited for each other for an hour.
In its literal, spatial meaning, 'aufeinander' (on top of each other) is often used with verbs like 'legen' (to put/lay), 'stapeln' (to stack), or 'liegen' (to lie) to express that things are positioned one on top of another.
Stapeln Sie die Teller bitte vorsichtig aufeinander.
Please stack the plates carefully on top of each other.
To express a direct sequence in time, 'aufeinander' (one after another) is almost always combined with the verb 'folgen' (to follow). It then means that something happens immediately after something else.
Die Termine folgen heute sehr dicht aufeinander.
The appointments are following very closely one after another today.
against each other
Aufeinander describes mutual alignment in movement, for example when two vehicles are moving toward each other. Gegeneinander emphasizes contact or a collision in opposite directions. Before the collision, they move aufeinander zu (toward each other); at the moment of impact, they collide gegeneinander.
Die beiden Einkaufswagen rollen ungebremst aufeinander zu.
The two shopping carts roll toward each other without slowing down.
Kurz darauf prallen die beiden Einkaufswagen gegeneinander.
Shortly afterward, the two shopping carts collide with each other.
