Collective instabilities in intense charged particle beams described self-consistently by the Vlasov-Maxwell equations are studied using a 3D multispecies nonlinear perturbative particle simulation method. The electron-proton (e-p) two-stream instability is observed in the simulations carried out with the newly-developed Beam Equilibrium Stability and Transport (BEST) code. This code provides an effective numerical tool to investigate collective instabilities, periodically-focused beam propagation in alternating-gradient focusing fields, halo formation, and other important nonlinear processes in intense beam propagation. ©1999 American Institute of Physics.