A nonlinear shallow-water model on the sphere is used to study barotropic aspects of the formation of twin tropical disturbances by Madden–Julian oscillation (MJO) convection. In the model, the effect of MJO convection upon the lower-tropospheric tropical circulation was simulated by an eastward moving, meridionally elongated mass sink straddling the equator. The intensity and propagation speed of the mass sink were chosen to simulate observations that MJO convection intensifies while nearly stationary in the eastern equatorial Indian Ocean, weakens while moving eastward over the Maritime Continent, again intensifies once it reaches the west Pacific Ocean, and finally becomes stationary and dies off near the date line. This mass sink produced twin cyclones in the two regions where it was stationary, namely, where it was initially turned on and where it was turned off. In addition, the mass sink produced two zonally elongated cyclonic potential vorticity anomalies straddling the equator in the region where it propagated eastward. It is proposed that MJO convection produces twin tropical disturbances in the two regions where it is nearly stationary, namely, its region of formation in the eastern Indian Ocean and its region of decay near the date line. Additional tropical disturbances may arise from the breakdown of the elongated shear regions produced by the eastward propagating MJO convection. In addition, a series of initial value experiments was performed to determine the conditions under which twin cyclones become so strongly coupled that they propagate directly eastward as a cyclone pair. Apparently, such movement requires the cyclones to be so close together that the situation rarely, if ever, occurs in nature.