We have studied &(1+1') ;-photon dissociation of the NaH molecule (ab initio) from the v = 0 level of the ground electronic state (X 1Σ+) to the repulsive B 1Π state via the bound intermediate A 1Σ+ state. By solving the one-dimensional time-dependent Schrödinger equation for nuclear motion using the Fourier grid technique we have shown that the maximum of the &(1+1') ;-photon dissociation cross section and the shape of the dissociation spectrum can be controlled by controlling the time delay between the two photoexcitation processes, i.e. bound–bound excitation by the first photon and bound–continuum excitation by the second photon respectively. The oscillation of the maximum of the dissociation cross section with time delay between the two pulses has been shown to be due to the excitation of different oscillating wavepackets at different delays from the intermediate A 1Σ+ state. It has also been shown that the dissociation spectrum depends on the duration and temporal profile of the femtosecond pulses used for excitation and hence dissociation can be controlled by choosing pulses of different shapes and duration. At a particular frequency of the second pulse, the dissociation cross section oscillates with time delay and this oscillation in the cross section can be used as a time-dependent quantum gate.