  We consider decay of metastable states of forced vibrations of a quantum
oscillator close to bifurcation points, where dissipation becomes effectively
strong. We show that decay occurs via quantum activation over an effective
barrier. The decay probability $W$ scales with the distance $\eta$ to the
bifurcation point as $|\ln W|\propto \eta^{\xi}$. The exponent $\xi$ is found
for a resonantly driven oscillator and an oscillator modulated at nearly twice
its eigenfrequency.
