
kandidieren
to run
To seek a political office, function, or position in order to be elected.
Sie kandidiert bei der nächsten Wahl für den Bundestag.
She is running for the Bundestag in the next election.
to run
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to run
To seek a political office, function, or position in order to be elected.
Sie kandidiert bei der nächsten Wahl für den Bundestag.
She is running for the Bundestag in the next election.

to be nominated
To apply for or be nominated for a prize, award, or membership.
Der Film kandidiert für den Oscar als bester ausländischer Film.
The film is nominated for the Oscar for best foreign film.
The verb 'kandidieren' (to run / to be nominated) belongs to the word family of 'der Kandidat' (the male candidate) and 'die Kandidatin' (the female candidate). The ending '-ieren' is typical of many verbs that come from foreign languages, and it is always conjugated regularly.
Der amtierende Bürgermeister hat viele Kandidaten gegen sich.
The incumbent mayor has many candidates running against him.
'Kandidieren' (to run / to be nominated) is often used with the prepositions 'für' (for) and 'als' (as). You run 'für' an office (accusative) and 'als' a certain person or role (nominative).
Er kandidiert für den Posten des Schatzmeisters.
He is running for the position of treasurer.
In a political context, 'kandidieren' (to run) is often combined with 'für ein Amt' (for an office), 'für eine Partei' (for a party), or 'bei einer Wahl' (in an election). You can also run 'gegen' (against) another person.
Bei der nächsten Kommunalwahl kandidiert er für die Grünen.
In the next local election, he is running for the Greens.
In this meaning, the word is used in the context of art, culture, or science. Typical phrases are 'für einen Preis kandidieren' (to be nominated for a prize) or 'für eine Auszeichnung kandidieren' (to be nominated for an award).
Die Autorin kandidiert mit ihrem neuen Roman für den Deutschen Buchpreis.
The author is nominated for the German Book Prize with her new novel.
to apply for
Both words can be associated with a position in an organization. „Beantragen“ refers to formally applying for admission or approval, whereas „kandidieren“ means putting yourself forward for a position that others will decide on. You beantragt membership, but kandidiert for an office.

Mara kandidiert für einen Sitz im Vorstand des Sportvereins.
Mara is running for a seat on the sports club's board.
Mara beantragt die Mitgliedschaft im Sportverein.
Mara applies for membership in the sports club.