  For a partial order $\preceq$ on a set X and an equivalency relation S
defined on the same set X we derive a necessary and sufficient condition for
the existence of such a total preorder on X whose asymmetric part contains the
asymmetric part of the given partial order $\preceq$ and whose symmetric part
coincides with the given equivalence relation S. This result generalizes the
classical Szpilrajn theorem on extension of a partial order to a perfect
(linear) order.
