  We present a one-dimensional model for diffusion in a fluctuating lattice;
that is a lattice which can be in two or more states. Transitions between the
lattice states are induced by a combination of two processes: one periodic
deterministic and the other stochastic. We study the dynamics of a system of
particles moving in that medium, and characterize the problem from different
points of view: mean first passage time (MFPT), probability of return to a
given site ($P_{s_0}$), and the total length displacement or number of visited
lattice sites ($\Lambda$). We observe a double {\it resonant activation}-like
phenomenon when we plot the MFPT and $P_{s_0}$ as functions of the intensity of
the transition rate stochastic component.
