
zögern
to hesitate
To pause or wait for a moment before doing or saying something, often out of uncertainty, doubt, or indecision.
Er zögerte kurz, bevor er die Tür öffnete.
He hesitated briefly before opening the door.
to hesitate
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to hesitate
To pause or wait for a moment before doing or saying something, often out of uncertainty, doubt, or indecision.
Er zögerte kurz, bevor er die Tür öffnete.
He hesitated briefly before opening the door.

to delay
To consciously postpone or put off carrying out an action or making a decision.
Bei diesen Symptomen sollten Sie nicht mit dem Arztbesuch zögern.
With these symptoms, you should not delay seeing a doctor.
'Zögern' (to hesitate) is often used in two patterns. You can say 'zögern, etwas zu tun' (to hesitate to do something; with an infinitive and 'zu'). You can also say 'mit etwas zögern' (to delay something; with the preposition 'mit' and dative).
Sie zögerte, die Wahrheit zu sagen.
She hesitated to tell the truth.
The expression 'ohne zu zögern' (without hesitating) is very common and means 'immediately' or 'without delay.' It expresses that someone carries out an action without doubt or pause.
Er half der alten Dame ohne zu zögern über die Straße.
He helped the old lady across the street without hesitating.
The negative request 'Zögern Sie nicht, ...' (Do not hesitate to ...) is a very polite and common way to encourage someone to do something, for example to get in touch.
Zögern Sie nicht, bei Fragen anzurufen.
Do not hesitate to call if you have any questions.
to sway / fluctuate / waver
Zögern mainly means delaying an action or decision. Schwanken, by contrast, describes going back and forth between different opinions, decisions, or feelings. Someone who has not acted yet zögert; someone who switches between options schwankt, although both can occur together.

Vor der Anmeldung zögerte Lara noch einige Minuten, obwohl sie den Kurs besuchen wollte.
Lara hesitated for a few more minutes before registering, even though she wanted to take the course.
Bei der Anmeldung schwankte Lara zwischen dem Sprachkurs am Montag und dem Kurs am Dienstag.
While registering, Lara wavered between the language course on Monday and the one on Tuesday.