  This work deals with the homogenization of an initial- and boundary-value
problem for the doubly-nonlinear system $$ D_t w -\nabla\cdot \vec z =
\nabla\cdot \vec h(x,t,x/\varepsilon), \qquad w\in \alpha(u,x/\varepsilon),
\qquad \vec z\in \vec\gamma(\nabla u,x/\varepsilon). $$ Here $\varepsilon$ is a
positive parameter, and the prescribed mappings $\alpha$ and $\vec\gamma$ are
maximal monotone with respect to the first variable and periodic with respect
to the second one.
  The two inclusions are here formulated as null-minimization principles, via
the theory of Fitzpatrick [MR 1009594]. As $\varepsilon\to 0$, a two-scale
formulation is derived via Nguetseng's notion of two-scale convergence, and a
(single-scale) homogenized problem is then retrieved.
