We have simulated the dynamics of a two-dimensional system of hard ellipses by event-oriented molecular dynamics in microcanonical NVE ensemble. Various quantities, namely longitudinal and transverse velocity auto-correlation functions, translational and rotational diffusion mean-squared displacements, pressure, intermediate self-scattering function, radial distribution function, and angular spatial correlation, have been obtained and their dependence on packing fraction is characterized. Despite absence of prominent positional ordering, the orientational degree of freedom behaves nontrivially and exhibits interesting features. Slowing down is observed in the angular part of the motion near isotropic-nematic phase transition. It is shown that above a certain packing fraction the rotational mean-squared displacement exhibits a three-stage temporal regime including a plateau. Comparison to 2D system of hard needles is made and it is shown that from positional viewpoint, the ellipse system is more ordered.