Seems like it was the carb. The float appeared to be sticking a bit, so I took it all apart and cleaned it. Actually, at first I noticed it was running way too rich. After fiddling with the carb a bit, then it was running way too lean. I then took it apart and cleaned it, and for the time being at least, runs fine again. I'll buy a replacement carb, and if it every acts up again, i'll be switching it.
Thanks for your help