A theory is presented to describe the orientational dynamics of block copolymer lamellar phases subjected to steady shear flow. By modifying an earlier theory by Cates and Milner to incorporate different viscosities of the pure block components, as well as restoring some neglected couplings between the mean composition pattern and composition fluctuations about the mean, it is demonstrated that the qualitative features of experimental observations on sheared poly(ethylene-propylene)-poly(ethylethylene) diblock copolymer melts can be reproduced. The theory may also be applicable to certain lyotropic lamellar phases assembled from nonpolymeric surfactants.