The spatial evolution of a velocity- or density-modulated ion beam is calculated for stable and unstable ion beam plasma systems, using the linearized Vlasov-Poisson equations. The propagation properties are found to be strongly dependent on the form of modulation. In the case of velocity modulation, the perturbation grows initially and then shows a periodic change of amplitude along the beam, while in the case of a density modulation only an instability causes growth. The findings are in agreement with experimental results obtained by SATO et al. (1977).