  We obtain necessary and sufficient conditions when a pseudocompact
paratopological group is topological. (2-)pseudocompact and countably compact
paratopological groups that are not topological are constructed. It is proved
that each 2-pseudocompact paratopological group is pseudocompact and that each
Hausdorff \sigma-compact pseudocompact paratopological group is a compact
topological group. Our particular attention is devoted to periodic and
topologically periodic pseudocompact paratopological groups.
