  We study groups acting on CAT(0) square complexes. In particular we show if Y
is a nonpositively curved (in the sense of A. D. Alexandrov) finite square
complex and the vertex links of Y contain no simple loop consisting of five
edges, then any subgroup of the fundamental group of Y either is virtually free
abelian or contains a free group of rank two. In addition we discuss when a
group generated by two hyperbolic isometries contains a free group of rank two
and when two points in the ideal boundary of a CAT(0) 2-complex at Tits
distance $\pi$ apart are the endpoints of a geodesic in the 2-complex.
