White moss/fur on newly germinating seeds

Some of my seedlings have started to develop a white furry moss. Is this something to be concerned about? I remember getting a little of this moss when growing some lavender from seed for a little while, or is this part of the germinating process for some seeds?
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What are you growing?
The moss os currently on some F1 Hybrid chilli's, radish seedlings, and on Sweetcorn (going from memory.. might have to check when I get home from work).
It could be the compost is too wet -is it on the seedlings or on the compost surface?
Compost surface... could well be the wet compost. Shall I just remove it?
Yes if you can and ease back on the watering it is a sign of too much humidity.
its been kind of damp so dont water too much, i use vermiculite with my compost, after sprinkling a layer of compost on seed i use perlite.