Abstract The author presents an explicit exact solution to the governing equations for geophysical equatorial waves in the β-plane setting. The solution describes equatorially trapped waves propagating eastward above the thermocline and beneath the near-surface layer where wind effects are confined. At great depths the water is still, while the transition toward the large-amplitude oscillation of the thermocline is accommodated by an eastward-flowing current. Above the thermocline a flow reversal occurs, with the underlying current flowing westward close to the layer where wind effects are confined.