Time overlap between two postdocs? Simply keep two affiliations or quit the first position earlier? My current postdoc position will end in few months, so I started to apply for another postDoc position abroad. Shortly, if I would get the second position, there might be about two months overlap between them. 

What is your advise on how to deal with it? What I am considering:


End the first job two months earlier, and start the new one. 
Keep both positions during those two months: start the full-time the
second one and continue the first one on weekends, until it "dies"
naturally.


I think the most honest would be the first option (opt#1). However, as my manuscripts were submitted for publication, I will work on them no matter where I end up (likely the second position). The finalization of those manuscripts is my main responsibility, and I cannot be sure about the each review processing time and schedule. 

In this case, I would get at least paid for my publication finalizing (opt#2), which would not happen if I will officially quit my first postdoc earlier (opt#1). And I can use two affiliations during the time overlap.

Should I notify my future employer about my postdocs position overlap and my potential plan to keep two affiliations?

My expertise is in ecology, therefore I am transferring neither extra secret information nor some commercial patents between positions.
Around here (in Nordic countries), many institutions and non-academic workplaces include terms about informing the employer of other work besides the one the contract is for. As such, I would be contractually obliged to inform the university that I am also emplyed (presumably full-time) by another institute. Since both of them would have a claim to my full time work, it would be unlikely that I could satisfy that requirement, I would expect them to not accept the situation.

In your case, I would discuss the situation with my current and future superior and give up one position at the same time as starting the other, so that I am only employed once. At least in mathematics, there is typically flexibility to adjust the starting and ending times of the contracts by a month or two, as convenient for everyone.

Also, you can just resign. Out of courtesy, as Buffy noted, please make a clean exit where you finish as much unfinished business as possible and take care that all duties you have (teaching, running a seminar, etc.) are transferred to someone else. Make sure your data or code is available and documented and your collaborators and superiors know where to find it, if this is relevant in your field and country.



At least in pure and applicable mathematics, it is expected for one to continue previous research projects at the new institute. This might be very different if you are hired for a concrete job as a part of a team, but I would guess that most academic jobs allow a measure of flexibility in the matter, as outside collaborations are usually valued. Discuss with your future supervisor if you are in doubt.