  In this article, we characterize nearly invariant subspaces of finite defect
for the backward shift operator acting on the vector-valued Hardy space which
is a vectorial generalization of a result of Chalendar-Gallardo-Partington
(C-G-P). Using this characterization of nearly invariant subspace under the
backward shift we completely describe the almost invariant subspaces for the
shift and its adjoint acting on the vector valued Hardy space.
