  We study {\em sign-restricted matrices} (SRMs), a class of rectangular $(0,
\pm 1)$-matrices generalizing the alternating sign matrices (ASMs). In an SRM
each partial column sum, starting from row 1, equals 0 or 1, and each partial
row sum, starting from column 1, is nonnegative. We determine the maximum
number of nonzeros in SRMs and characterize the possible row and column sum
vectors. Moreover, a number of results on interchange operations are shown,
both for SRMs and, more generally, for $(0, \pm 1)$-matrices. The Bruhat order
on ASMs can be extended to SRMs with the result a distributive lattice. Also,
we study polytopes associated with SRMs and some relates decompositions.
