Today I got a Philips NMS 8250, and it seems, that the battery of its realtime clock is empty, as it doesn't increase the time, when the computer is not switched on.
So my question is:
- is the battery rechargeable, so should I switch on the computer for a longer periode?
- if not, can I replace it?

afaik, You need to replace the battery.

I don't think it's rechargable. But IIRC (and it's the same as my 8280), it's a common battery type and should be easy to replace.

You can try to see whether the thing's rechargeable -- just switch on your 8250, wait 24h, set the correct time, power off and reboot after 10 minutes. If this still results in a reset time, then it's time to change your battery . With the 8250 it's, luckily, an easy job: unscrew the top of the case (7 screws), then the disk compartiment, which is, afaik, 4 screws, some ribbon cables, etc. Then you're already able to see the battery, it's a yellowish penlite-like thing. I think even the + and - signs are applied onto the mainboard. Cut the two connections to the mainboard, and resolder the replacement. But for now, it's just finding a replacement

Good luck!

All european MSX2 machines have rechargeable (NiCd) RTC batteries. Problem is you can't recharge them infinitely. After a bunch of years or recharges it'll need to be replaced.