  In this paper, we report the bifurcations of mode-locked periodic orbits
occurring in maps of three or higher dimensions. The `torus' is represented by
a closed loop in discrete time, which contains stable and unstable cycles of
the same periodicity, and the unstable manifolds of the saddle. We investigate
two types of `doubling' of such loops: in (a) two disjoint loops are created
and the iterates toggle between them, and in (b) the length of the closed
invariant curve is doubled. Our work supports the conjecture of Gardini and
Sushko, which says that the type of bifurcation depends on the sign of the
third eigenvalue. We also report the situation arising out of Neimark-Sacker
bifurcation of the stable and saddle cycles, which creates cyclic closed
invariant curves. We show interesting types of saddle-node connection
structures, which emerge for parameter values where the stable fixed point has
bifurcated but the saddle has not, and vice versa.
