In this paper, we prove well-posedness of the one dimensional Gurevich-Zybin system in Besov spaces Bp,rs. This will imply the existence and uniqueness of solutions in the aforementioned spaces along with the continuity of the data-to-solution map, provided that the initial data belong to Bp,rs. We also establish persistence properties of solutions by showing that strong solutions to the Gurevich-Zybin system decay at infinity in the spatial variable, provided that the initial data do. Furthermore, it is shown that the system exhibits finite speed of propagation in the sense that if the initial data are endowed with compact support, then the solution carries this support along particle trajectories. As a concluding note, we discuss blow-up criterion for solutions.