A plasma wave with an oscillating amplitude and phase occurs in two commonly studied situations, the beam‐plasma interaction and the launching of a large‐amplitude wave in a Maxwellian plasma. Electron motion in such a wave is either regular or stochastic. Theoretical study shows that regular motion can exhibit a phase‐locking effect, which explains the persistence of amplitude oscillations observed in simulations and experiments. An additional (’’test’’) wave of moderate amplitude can prevent phase‐locking, causing stochastic motion instead, and thereby destroy the amplitude oscillations. The effects studied are also relevant to the theory of sideband instability.