  Almost paracontact metric manifolds are the famous examples of almost para-CR
manifolds. We find necessary and suffcient conditions for such manifolds to be
para-CR. Next we examine these conditions in certain subclasses of almost
paracontact metric manifolds. Especially, it is shown that the normal almost
paracontact metric manifolds are para-CR. We establish necessary and suffcient
conditions for paracontact metric manifolds as well as for almost
paracosymplectic manifolds to be para-CR. We find also basic curvature
identities for para-CR paracontact metric manifolds and study their
consequences. Among others, we prove that any para-CR paracontact metric
manifold of constant sectional curvature and of dimension greather than tree
must be para-Sasakian and its curvature equal to minus one. The last assertion
do not hold in dimension tree. Moreover, we show that a conformally flat
para-Sasakian manifold is of constant sectional curvature equal to minus one.
New classes of examples of para-CR manifolds are established.
