Moisture and microbes must have gotten in somehow. You have to find the entrance point and seal it. Any excess moisture in the wood has to be given time to evaporate. Once the moisture content of the area is reduced sufficiently the microbes will die but the black lines will remain. It's really hard to get rid of the black stuff without sanding. I would try a mild bleach like hydrogen peroxide to see if that will lighten the line without bleaching the wood.
Also, I found trying to keep a crack in a veneer from reopening difficult. If the veneer is cracked it would be wise to try to get epoxy in there to stabilize the edges.

: My boat's a couple of years old, and in the last year it's grown what appears
: to be mold in a couple of spots. It's black lines that I can actually feel
: under the epoxy. Any suggestions on what to do? I'd hate to sand right
: thru the top layer of okume.

: Thanks,
: jim