  We extend a classical theorem by H. Lewy to planar $\sigma$-harmonic
mappings, that is mappings $U$ whose components $u^1$ and $u^2$ solve a
divergence structure elliptic equation ${\rm div} (\sigma \nabla u^i)=0$ , for
$i=1,2$. A similar result is established for pairs of solutions of certain
second order non--divergence equations.
