An accurate theory of two-photon dissociation with strong laser pulses, which goes beyond the adiabatic approximation, is developed. Criteria for adiabatic behavior in two photon dissociation (enabling via adiabatic passage the complete population transfer to the continuum), are derived. We obtain the minimal pulse duration needed to ensure adiabaticity as a function of the field intensities and detuning. In addition, we develop a simple, rapidly converging, iterative scheme, built on the adiabatic approximation, for the exact solution of the two-photon dissociation problem. Each iteration step requires a computational effort that scales as N-2 (N being the system dimension) for full matrices, or N log N for sparse matrices. The iterative scheme is tested by comparing it to the Runge-Kutta-Merson direct integration algorithm. It is found to work well even when the adiabatic approximation fails completely.