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Hi,

What should you say?

There will be a follow-up on your homework

or

There will be a follow-up of your homework?

Are both okay? Or are both incorrect?

What should you say in that case?

Lena
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Lena,

according to a number of dictionaries and reference books on English usage, follow-up meaning a book, film, or article that is based on or develops an earlier one (=sequel) is used with to, eg, He's currently working on a follow-up to his last novel. However, follow-up can have a slightly different meaning, as in a follow-up of the report on smoking hazards, where of is chiefly used. Concerning your example, I would recommend using either of or to, with of being more acceptable.

Respectfully, Gleb Chebrikoff.
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"On" is fine. I would use "on" or "to".

I also disagree that "of" is more acceptable. (according to COCA it is not).

Anyway, we would do better to wait for native speakers to chime in.