We present several models of time fluctuating media with finite memory, consisting in one and two-dimensional lattices, the Modes of which fluctuate between two internal states according to a Poisson process. A particle moves on the lattice, the diffusion by the Modes depending on their internal state. Such models can be used for the microscopic theory of reaction constants in a dense phase, or for the study of diffusion or reactivity in a complex medium. In a number of cases, the transmission probability of the medium is computed exactly; it is shown that stochastic resonances can occur, an optimal transmission being obtained for a convenient choice of parameters. In more general situations, approximate solutions are given in the case of short and moderate memory of the obstacles. The diffusion in an infinite two-dimensional lattice is studied, and the memory is shown to affect the distribution of the particles rather than the diffusion law. (author). 25 refs, 5 figs