Generalized Taylor dispersion theory (GTDT) is extended with the goal of obtaining a macroscale description of the transport processes in cases of time-periodic zero-mean convection in a homogeneous shear flow under the action of a spatially-uniform force field. The resulting scheme is uniformly valid throughout the frequency spectrum provided that particle hydrodynamic properties may be obtained from the solution of appropriate steady Stokes problems.The extended theory is illustrated in the context of the sedimentation of Brownian axisymmetric particles in time-periodic homogeneous shear under the action of time-periodic external force. Explicit results are presented for the limiting case when particle rotary oscillations induced by the time-periodic homogeneous shear are small. (The rotary Peclet numbers need not, however, be small.).