  A theorem of Cantat and Urech says that an analog of the classical Tits
alternative holds for the group of birational automorphisms of a compact
complex Kaehler surface. We established in our previous paper the following
Tits-type alternative: if X is a toric affine variety and G is a subgroup of
Aut(X) generated by a finite set of unipotent subgroups normalized by the
acting torus then either G contains a nonabelian free subgroup or G is a
unipotent affine algebraic group. In the present paper we extend the latter
result to any group G of automorphisms of a complex affine surface generated by
a finite collection of unipotent algebraic subgroups. It occurs that either G
contains a nonabelian free subgroup or G is a metabelian unipotent algebraic
group.
