  This paper deals with the homogenization of the reaction-diffusion equations
in a domain containing periodically distributed holes of size $\varepsilon$,
with a dynamical boundary condition of reactive-diffusive type, i.e., we
consider the following nonlinear boundary condition on the surface of the holes
$$ \nabla u_\varepsilon \cdot \nu+\varepsilon\,\displaystyle\frac{\partial
u_\varepsilon}{\partial t}=\varepsilon\,\delta
\Delta_{\Gamma}u_\varepsilon-\varepsilon\,g(u_\varepsilon), $$ where
$\Delta_{\Gamma}$ denotes the Laplace-Beltrami operator on the surface of the
holes, $\nu$ is the outward normal to the boundary, $\delta>0$ plays the role
of a surface diffusion coefficient and $g$ is the nonlinear term. We generalize
our previous results (see [3]) established in the case of a dynamical boundary
condition of pure-reactive type, i.e., with $\delta=0$. We prove the
convergence of the homogenization process to a nonlinear reaction-diffusion
equation whose diffusion matrix takes into account the reactive-diffusive
condition on the surface of the holes.
