  Let M be an almost complex manifold equipped with a Hermitian form such that
its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly
Kahler manifold. We prove that any connected component of the moduli space of
pseudoholomorphic curves on M is compact. This can be used to study
pseudoholomorphic curves on a 6-dimensional sphere with the standard
(G_2-invariant) almost complex structure.
