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