The stability of periodic arrays of Mallier–Maslowe or Kelvin–Stuart vortices is discussed. We derive with the energy‐Casimir stability method the nonlinear stability of this solution in the inviscid case as a function of the solution parameters and of the domain size. We exhibit the maximum size of the domain for which the vortex street is stable. By adapting a numerical time‐stepping code, we calculate the linear stability of the Mallier–Maslowe solution in the presence of viscosity and compensating forcing. Finally, the results are discussed and compared to a recent experiment in fluids performed by Tabelingetal. [Europhy. Lett.3, 459 (1987)]. Electromagnetically driven counter‐rotating vortices are unstable above a critical electric current, and give way to co‐rotating vortices. The importance of the friction at the bottom of the experimental apparatus is also discussed. ©1996 American Institute of Physics.