A theoretical and experimental study of Trivelpiece–Gould waves propagating in a magnetized plasma column is presented in this paper. In the experiments, these waves are excited by a radio frequency (rf) source, which also serves to create the plasma. Observation of nonlinear effects includes space and time recurrence effects, a wave spectrum containing a large number (up to 25) harmonics, and low‐frequency sidebands. The theoretical model explains the recurrence effects as a consequence of multiple nonlinear interactions between the fundamental wave and its harmonics. A good agreement is found between theory and the experiments.