  Let M be an almost Hermitian manifold of dimension greater or equal to 6. The
following theorems are proved: Theorem 1. If M is of pointwise constant
{\theta}-holomorphic sectional curvature for a number {\theta} in (0,{\pi}/2)
then M is of constant sectional curvature or a K\"ahler manifold of constant
holomorphic sectional curvature. Theorem 2. If M is of pointwise constant
antiholomorphic sectional curvature and M is an RK-manifold (or AH3-manifold),
then M is of constant antiholomorphic sectional curvature.
