A simple, practical, analytical model is developed of the drift induced by weakly asymmetrical progressive waves in the bottom boundary layer above rippled and very rough beds. Above such beds, momentum transfer is dominated not by random turbulence, but by the well-organized process of vortex shedding, which is characterized here by a strongly time-varying convective eddy viscosity K. The one-dimensional wave boundary layer model proposed is consistent with the presence of Stokes' second-order waves in the free-stream flow. The solution for the Eulerian drift is characterized by a pronounced near-bed jet in the direction of wave advance, beneath a layer extending to the edge of the boundary layer in which the drift is in the opposite direction. An empirical approach involving five published laboratory data sets is used to estimate the coefficient defining the asymmetrical time-varying component of K above rippled and very rough beds. The resulting standard model is then compared both with measurements of the drift at the edge of the wave boundary layer and also with measured drift profiles. Good agreement is found for ranges of wave steepness and relative bed roughness of practical importance. ¿ 1999 American Geophysical Union