The time evolution of space-charge field gratings in photorefractive media is derived for a simple two-level electron-hole-transport model. At one level, charge transfer occurs by electron transport, and at the other, by hole transport, thus leading to the formation of complementary gratings. If the characteristic lifetimes of the gratings differ significantly, extended-lifetime gratings are possible. The role of the applied electric field in the evolution of such gratings is examined, and limiting cases are considered. The results of the derivation are compared with examples of complementary gratings in the literature. © 1990 Optical Society of America.