A variational approach is used to examine the possibility of bistable behavior in a two‐component metal‐dielectric composite medium with a periodic microstructure where one component has a Kerr‐ type field dependent part in the dielectric constant &egr; while the field independent part of &egr; in both materials is in general complex. It is shown that under certain conditions bistable behavior can occur even though the field dependent nonlinearity is weak everywhere. This is achieved by operating the material sufficiently close to one of its sharp quasi‐static, microgeometric electrical resonances. The physical characteristics of the threshold intensity are worked out and considerations made on how to optimize the chances for observing optical bistability in such a material. ©1995 American Institute of Physics.