The spatial variation and degree of anisotropy of the permeability field (k) is an important parameter affecting the dynamics of convective fluid flow in saturated geologic media. We report results from time-dependent, two-dimensional numerical simulations, with constant fluid properties, for k fields that are anisotropic, layered or both. Streamlines and isotherms are given for domains with permeable and impermeable tops for Ra (100--300), kz/kx (0.33--40) and for a system with two isotropic layers of equal height, kt/kb (0.1--10). The kinetic energy (KE) and Nusselt number (Nu) monotonically decrease as kz/kx increases at constant Rayleigh number, defined with respect to kz. In two-layer systems, KE increases linearly and Nu increases asymptotically as kt/kb increases at constant Rayleigh number, defined with respect to kb. For otherwise identical cases, KE and Nu are greater for permeable top than impermeable top boundary conditions. Time to steady-state is inversely proportional to KE1/2. Results are also presented for k fields that are both anisotropic and layered as an analog to oceanic crust permeability. ¿ American Geophysical Union 1990