A mechanism for producing long-period oscillations of both the wave and zonal-flow components in a two-layer baroclinic system is described. The mechanism hinges on two fundamental properties. First, when the planetary β-effect is sufficiently large, two fundamental linearly-unstable waves with adjacent azimuthal wavenumbers can both equilibrate to non-zero finite-amplitude. Because these adjacent wavenumbers have different frequenciesf1andf2when on the β-plane, interference between the fundamental instabilities will generate an apparent periodic fluctuation in the wave field with a lower frequencyf2-f1, but there is no direct periodic forcing of the zonal flow. Secondly, however,nonlineargeneration of higher-order sidebands by the two fundamentals, coupled with back interactions on the fundamentals themselves will generate azonal flow vacillationwith frequencyn2f1-n1f2, wheren1andn2are the fundamental wavenumbers. This vacillation mechanism is first illustrated through truncated spectral model calculations. These are then shown to successfully predict a number of laboratory experimental observations of low-frequency zonal-flow oscillations.