  We consider Zimmer's program of lattice actions on surfaces by PL
homomorphisms. It is proved that when the surface is not the torus or Klein
bottle the action of any finite-index subgroup of SL(n,Z), n>4, (more generally
for any 2-big lattice), factors through a finite group action. The proof is
based on an establishment of a PL version of Reeb-Thurston's stability.
