Longitudinal vortices with axes in the direction of a mean shear flow can arise due to body force instabilities associated with heating or centrifugal effects. In this paper we are concerned with possible stabilization or destabilization of such instabilities by means of a controlled flow oscillation in the spanwise direction. For the heated case, stabilization occurs up to the values of Rayleigh and Reynolds numbers at which streamwise two-dimensional disturbances become critical. For the centrifugal case, stabilization occurs only for sufficiently large values of the Reynolds number associated with the spanwise oscillation; for smaller values, destabilization occurs. ©1997 American Institute of Physics.