nacheinander
one after another
Describes an order in which one action or event follows another; one after the other.
Die Redner traten nacheinander ans Pult.
The speakers stepped up to the podium one after another.

one after another
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one after another
Describes an order in which one action or event follows another; one after the other.
Die Redner traten nacheinander ans Pult.
The speakers stepped up to the podium one after another.

The word is made up of 'nach' (after) and 'einander' (one another). So it literally means that something happens 'one after the other.'
Die Kinder gingen nacheinander auf die Rutsche.
The children went down the slide one after another.
As an adverb, 'nacheinander' (one after another) usually comes after the conjugated verb. When it stands at the beginning of the sentence, the verb follows directly after it in position 2.
Wir haben die Aufgaben nacheinander bearbeitet.
We worked through the tasks one after another.
'Nacheinander' (one after another) is often used with verbs that describe a sequence of actions, such as 'eintreten' (to enter), 'sprechen' (to speak), 'bearbeiten' (to work through/process), or 'ankommen' (to arrive).
Die Bewerber wurden nacheinander zum Gespräch gebeten.
The applicants were invited to the interview one after another.
simultaneously / at the same time
'gleichzeitig' and 'nacheinander' describe two different time orders. You use 'gleichzeitig' when things happen at the same moment. You use 'nacheinander' when one thing happens first and then the next. This contrast is very useful for appointments, tasks, or people. If everyone speaks 'gleichzeitig', you understand very little. If everyone speaks 'nacheinander', there is a clear order.

Beim Termin werden die Kundinnen nacheinander aufgerufen.
At the appointment, the customers are called in one after another.
Bei der Veranstaltung starten zwei Workshops gleichzeitig.
At the event, two workshops start at the same time.