  A general study of minimal surfaces of the Riemannian product of two spheres
S^2xS^2 is tackled. We stablish a local correspondence between (non-complex)
minimal surfaces of S^2xS^2 and certain pair of minimal surfaces of the sphere
S^3. This correspondence also allows us to link minimal surfaces in S^3 and in
the Riemannian product S^2xR. Some rigidity results for compact minimal
surfaces are also obtained.
