  In this article we study isometric immersions of nearly K\"ahler manifolds
into a space form (specially Euclidean space) and show that every nearly
K\"ahler submanifold of a space form has a totally umbilic foliation whose
leafs are 6-dimensional nearly K\"ahler manifolds. Moreover using this
foliation we show that there is no non-homogeneous 6-dimensional nearly
K\"ahler submanifold of a space form. We prove some results towards a
classification of nearly K\"ahler hypersurfaces in standard space forms.
