Large scale one-dimensional hybrid simulations of a quasi-parallel (&THgr;Bn=20¿) high Mach number (MS~5) collisionless shock have been performed. The numerical system is 500 ion inertial lengths long and the shock has been followed up to 150 ion gyroperiods. The omnidirectional distribution function of the ions in the region upstream of the shock exhibits a high energy tail. About 5% of all ions in the upstream region have a velocity exceeding the shock ram velocity. Phase space contour plots show that these ions are diffuse. These ions are accelerated to high velocities during their first encounter with the shock. They stay very close to the shock for an extended period of time, about 50 gyroperiods, and experience the electric and magnetic field near the constantly reforming shock. Although the electric field at the particle position is highly fluctuating, the particle motion leads to a net energy gain. These particles may constitute a seed particle population for a first order Fermi process. The initial state of such a Fermi process can indeed be seen: some particles escape upstream, are turned back by the upstream waves and recross the shock, thus increasing their energy even further. ¿ American Geophysical Union 1990