  In this paper we analyse Abelian diagonal orthogonally transitive spacetimes
with spacelike orbits for which the matter content is a stiff perfect fluid.
The Einstein equations are cast in a suitable form for determining their
geodesic completeness. A sufficient condition on the metric of these spacetimes
is obtained, that is fairly easy to check and to implement in exact solutions.
These results confirm that non-singular spacetimes are abundant among stiff
fluid cosmologies.
