  We classify the second order, linear, two by two systems for which the two
fundamental theorems for planar harmonic mappings, the Rado'-Kneser-Choquet
Theorem and the H. Lewy Theorem, hold. They are those which, up to a linear
change of variable, can be written in diagonal form with the same operator on
both diagonal blocks. In particular, we prove that the aforementioned Theorems
cannot be extended to solutions of either the Lame' system of elasticity, or of
elliptic systems in diagonal form, even with just slightly different operators
for the two components.
