  A characterization of simplicial objects in categories with finite products
obtained by the reduced bar construction is given. The condition that
characterizes such simplicial objects is a strictification of Segal's condition
guaranteeing that the loop space of the geometric realization of a simplicial
space $X$ and the space $X_1$ are of the same homotopy type. A generalization
of Segal's result appropriate for bisimplicial spaces is given. This
generalization gives conditions guaranteing that the double loop space of the
geometric realization of a bisimplicial space $X$ and the space $X_{11}$ are of
the same homotopy type.
