  The stochastic resonance (SR) in bistable systems has been extensively
discussed with the use of {\it phenomenological} Langevin models. By using the
{\it microscopic}, generalized Caldeira-Leggett (CL) model, we study in this
paper, SR of an open bistable system coupled to a bath with a nonlinear
system-bath interaction. The adopted CL model yields the non-Markovian Langevin
equation with nonlinear dissipation and state-dependent diffusion which
preserve the fluctuation-dissipation relation (FDR). From numerical
calculations, we find the following: (1) the spectral power amplification (SPA)
exhibits SR not only for $a$ and $b$ but also for $\tau$ while the stationary
probability distribution function is independent of them where $a$ ($b$)
denotes the magnitude of multiplicative (additive) noise and $\tau$ expresses
the relaxation time of colored noise; (2) the SPA for coexisting additive and
multiplicative noises has a single-peak but two-peak structure as functions of
$a$, $b$ and/or $\tau$. These results (1) and (2) are qualitatively different
from previous ones obtained by phenomenological Langevin models where the FDR
is indefinite or not held.
