We deal with second-harmonic generation in chi((2)) nonlinear-optical
resonators such as prism or grating couplers. The theoretical study is
performed within the framework of a recently developed coupled-mode a
nalysis leading to a set of equations governing the amplitudes of pump
and second-harmonic frequency fields. We predict analytically that se
cond-harmonic generation in prism or grating couplers may lead to opti
cal bistability. We believe this to be the first demonstration of such
an effect in chi((2)) optical resonators.