We present a linear model of intraseasonal oscillations produced by the interaction of an atmosphere on an equatorial Beta-plane with a fixed ocean. Convection is treated as a means of rapidly redistributing in the vertical heat acquired from the sea surface, rather than as a heat source in and of itself. The model produces a spectrum of equatorially trapped oscillating instabilities, among which is an eastward-propagating wavenumber 1 disturbance with an intrinsic phase speed in the range of 4–20 m s−1, depending on the mean zonal wind, the surface exchange coefficients, the air-sea equivalent potential temperature difference, and the difference of absolute temperature across the depth of the lower troposphere. The three-dimensional structure of this mode is in excellent agreement with observations and recent numerical experiments concerning the 30–60 day oscillation. The phase speed and growth rate of the disturbances depend only on conditions at the equator, while their meridional structure varies with meridional gradients of mean zonal wind, sea surface temperature, and the depth of the moist convective layer. Momentum fluxes by the waves may serve to maintain mean easterlies at the equator. The model also predicts nongeostrophic oscillations with generally shorter periods of around one week.