We consider surfaces M2 immersed in En c × R, where En c is a simply connected n-dimensional complete Riemannian manifold
with constant sectional curvature c 6= 0, and assume that the mean curvature vector of the immersion is parallel in the normal bundle.
We consider further a Hopf-type complex quadratic form Q on M2, where the complex structure of M2 is compatible with the induced metric. It is not hard to check that Q is holomorphic (see [3], p.289). We will use this fact to give a reasonable description of immersed surfaces in En c ×R that have parallel mean curvature vector.