  We describe a new mechanism of tunneling between period-two vibrational
states of a weakly nonlinear parametrically modulated oscillator. The tunneling
results from resonant transitions induced by the fast oscillating terms
conventionally disregarded in the rotating wave approximation (RWA). The
tunneling amplitude displays resonant peaks as a function of the modulation
frequency; near the maxima it is exponentially larger than the RWA tunneling
amplitude.
