  We study bifurcation mechanisms for the appearance of hyperchaotic attractors
in three-dimensional diffeomorphisms, i.e., such attractors whose orbits have
two positive Lyapunov exponents in numerical experiments. In order to possess
this property periodic orbits belonging to the attractor should have
two-dimensional unstable invariant manifolds. For realization of this
possibility, we propose several bifurcation scenarios that include cascades of
both supercritical period-doubling bifurcations with saddle periodic orbits and
supercritical Neimark-Sacker bifurcations with stable periodic orbits, as well
as various combinations of these cascades. In the paper, these scenarios are
illustrated by an example of the three-dimensional Mir\'a map.
