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More clearly;

Is it possible to apply with a proposal like "I want to make international publications based on my PhD Thesis during my post-doc"

or

Does someone have to formulate an entirely new research question/proposal in the application?

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    This is extremely field-dependent, country-dependent, advisor-dependent, trainee-dependent, etc. – Bryan Krause Jan 24 '19 at 15:53
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Is it possible to apply with a proposal like "I want to make international publications based on my PhD Thesis during my post-doc"

This is appropriate if you want to pursue a post-doc with your PhD advisor, or you want to pursue a post-doc with an advisor that will allow you to do whatever you want. It is inappropriate if the advisor has their own research agenda.

Does someone have to formulate an entirely new research question/proposal in the application?

This is appropriate if the advisor doesn't have their own agenda.

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Postdoctoral fellowships come in all shapes and sizes.

It is often good to play to your strengths while keeping an eye towards where you want to get to. Some postdoctoral positions are very task oriented e.g. help run a lab doing X for 2 years. Others are more open ended. If you’re going for the former then it would be good to show how you’re the right person for the job. If it’s open ended then you may want to emphasize your capability to expand to new fields, hopefully those that your host is interested in.

It’s important to also focus on more “grownup” skills like managing students and writing grants, which may be expected of you.

Good luck!

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You need to show how your prior research is relevant to the field of research that falls within the scope of the advertised postdoc. Publishing papers in internationally recognized journals should be a unspoken assumption and you need not state it. Typically the professor will have already have a research agenda, and you need to make sure that it's a good fit for you before applying. If your prior research interest has no intersection with the professor's I would advise you not to apply at all. Conversely, you should highlight how your research interest aligns with the job scope of the postdoc.

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