Investigations have been made of plasma oscillations by studying space‐charge waves in velocity‐modulated electron beams. The convection current in a velocity‐modulated slowly‐drifting electron beam was measured as a function of distance from the modulating cavity. The experiments indicate that in the presence of an appreciable velocity spread, the fast space‐charge wave is damped while the slow space‐charge wave remains unattenuated. The measurements were made under conditions where the velocity spread is dominated by lens effects in the electron‐optical system. The results confirm qualitatively the theory of Berghammer and thus demonstrate the existence of the much disputed Landau damping.