  Deformation of morphisms along leaves of foliations define the tangential
foliation on the corresponding space of morphisms. We prove that codimension
one fo-liations having a tangential foliation with at least one non-algebraic
leaf are transversely homogeneous with structure group determined by the
codimension of the non-algebraic leaf in its Zariski closure. As an
application, we provide a structure theorem for degree three foliations on
$P^3$ .
