  We study special almost Kaehler manifolds whose curvature tensor satisfies
the second curvature condition of Gray. It is shown that for such manifolds,
the torsion of the first canonical Hermitian is parallel. This enables us to
show that every AK_2-manifold has parallel torsion. Some applications of this
result, concerning the existence of orthogonal almost Kaehler structures on
spaces of constant curvature are given.
