  We study solutions of the tree level string effective action in the presence
of the tachyon mode.We find that the 2-dim. static black hole is stable against
tachyonic perturbations.For a particular ansatz for the tachyon field we find
an exact solution of the equations of motion which exhibits a naked
singularity.In the case of static fields we find numerically that the full
system has a black hole solution,with the tachyon regular at the horizon.
