Longitudinal plane wave oscillations of electrons and ions described by the linearized Vlasov equation with no magnetic fields and coupled by Poisson's equation are examined for a wider class of distribution functions than previously analyzed. An expression is obtained for the time evolution of the electric field in terms of approximate wave contributions and a remainder. It is found that an electron plasma oscillation and an ion wave—either an ion acoustic wave or an ion plasma oscillation—are observable. For a short initial time interval coherent plasma oscillations are observable and persist if the ratio of Debye length to wavelength is small. For larger times, but not too large, ion waves are observable, and they persist for many periods if&rgr;−1 = {(T+/T−)[(k&lgr;−)2 + &ggr;0])12≪ 1, where&ggr;0is a positive constant of order unity determined by the electron distribution functions. The ion waves are thereafter exponentially damped into the incoherent background of the remaining contribution.