We study the phenomenon of stochastic resonance (SR) in a bistable sys
tem with internal colored noise. In this situation the system possesse
s time-dependent memory friction connected with noise via the fluctuat
ion-dissipation theorem, so that in the absence of periodic driving th
e system approaches the thermodynamic equilibrium state. For this non-
Markovian case we find that memory usually suppresses stochastic reson
ance. However, for a large memory time SR can be enhanced by the memor
y.