We consider the two-photon double ionization of atomic systems by ultrashort pulses. We examine the role of the electron correlations in three different regimes: the direct and the sequential regimes as well as a transient regime where the time of interaction is so short that the distinction between the direct and the sequential transitions becomes meaningless. Our analysis is based on an ab initio computational treatment that is time-dependent and based on a spectral method of configuration interaction type combined with Jacobi matrix calculations. This approach treats correctly the electron correlation both in the initial and final states as well as during the time propagation.