Two‐dimensional convection can become unstable to a mean shear flow. In three dimensions, with periodic boundary conditions in the two horizontal directions, this instability can cause the alignment of convection rolls to alternate between thexandyaxes. Rolls with their axes in they‐direction become unstable to a shear flow in thex‐direction that tilts and suppresses the rolls, but this flow does not affect rolls whose axes are aligned with it. New rolls, orthogonal to the original rolls, can grow, until they in turn become unstable to a shear flow. This behavior is illustrated through numerical simulations and low‐order models, and the sequence of local and global bifurcations is determined. ©1996 American Institute of Physics.