  We consider multiphoton resonance in the quantum driven nonlinear oscillator
in presence of high-order nonlinearities. Multiphoton resonances were
associated with anticrossings of the quasienergy levels, which leads to the
emergence of peaks and dips in the detuning dependence of the stable states
occupations. In presence of high-order nonlinearities the positions of
anticrossings acquire different shifts. Depending on the ratio between
high-order-nonlinearity-induced shift of the multiphoton resonance and Kerr
nonlinearity, the multiphoton resonance can acquire fine structure. We also
considered the effect of finite damping on the relative occupation of the
stable states. For different damping constants, we determined the quasienergy
region where the anticrossing effects strongly influence the system kinetics.
