A composite model is proposed to describe the time-dependent response of the Earth's lower crust. The motivation for such a model is twofold: First, new observations of widespread postseismic deformation indicate that the deep continental crust responds viscoelastically, having both long- and short-term decay times. Second, by any number of observationally based rationales, the lower crust is compositionally and structurally heterogeneous over many length scales. For heterogeneities that have much smaller characteristic lengths than the minimum deformation wavelength of interest, the aggregate rheology can be described by composite media theory. For wavelengths of the order of the thickness of the lower crust (≈25--40 km) and larger, composite theory may be applied to heterogeneities that are smaller than about several hundred meters, or equivalent to the vertical extent of a thick lower crustal mylonitic shear zone. The composite media theory developed here is constructed using both Eshelby-Mori-Tanaka theory for aligned generalized spheroidal inclusions and a generalized self-consistent method. The inclusions and matrix are considered to be Maxwellian viscoelastic: a rheology that is consistent with past homogeneous models of postseismic stress relaxation. The composite theory presented here introduces a transient response to a suddenly imposed stress field which does not appear in homogeneous Maxwell models. Analytic expressions for the amplitude and duration of the transient and for the effective long- and short-term viscosities of the composite are given which describe the sensitivity to inclusion concentration (ϕ), to shape, and to ratio of inclusion-to-matrix viscosity (R). ¿ American Geophysical Union 1996