  We study dynamics and bifurcations of two-dimensional reversible maps having
non-transversal heteroclinic cycles containing symmetric saddle periodic
points. We consider one-parameter families of reversible maps unfolding
generally the initial heteroclinic tangency and prove that there are infinitely
sequences (cascades) of bifurcations of birth of asymptotically stable and
unstable as well as elliptic periodic orbits.
