Several aspects of the short time dynamical behavior of Hamiltonian systems are studied. The case of persistence of regular motion in some parts of the chaotic region of the phase space is examined in relation to Nekhoroshev's theorem. A local rate of divergence is defined, and its relationship to the rate of decay of the time autocorrelation function of a phase space coordinate is shown. Finally a numerical method for studying the short time dynamics of Hamiltonian systems is proposed and tested.