The probabilities of transitions between the Fock states of two electromagnetic field modes under the influence of coupling between modes of finite duration are investigated. It is shown that the transition probability is a strongly oscillating function of the mode numbers of the photons. Under conditions in which the coupling frequency exceeds the geometric mean of the mode frequencies (strong coupling), large numbers of photons are excited in the mode with the lower frequency. The excitation of a two-dimensional radiation field oscillator and the ‘‘red’’ symmetry of the transition probabilities can be attributed to instability of the classical two-dimensional oscillator with strong mode coupling.