  We investigate minimal surfaces in products of two-spheres ${\mathbb
S}^2_p\times {\mathbb S}^2_p$, with the neutral metric given by $(g,-g)$. Here
${\mathbb S}^2_p\subset {\mathbb R}^{p,3-p}$ , and $g$ is the induced metric on
the sphere. We compute all totally geodesic surfaces and we give a relation
between minimal surfaces and the solutions of the Gordon equations. Finally, in
some cases we give a topological classification of compact minimal surfaces.
