  Motivated by the finiteness of the set of automorphisms Aut(X) of a
projective manifold X, and by Kobayashi-Ochiai's conjecture that a projective
manifold dim(X)-analytically hyperbolic (also known as strongly measure
hyperbolic) should be of general type, we investigate the finiteness properties
of Aut(X) for a complex manifold satisfying a (pseudo-) intermediate
hyperbolicity property. We first show that a complex manifold X which is
(dim(X) -- 1)-analytically hyperbolic has indeed finite automorphisms group. We
then obtain a similar statement for a pseudo-(dim(X) -- 1)-analytically
hyperbolic, strongly measure hyperbolic projective manifold X, under an
additional hypothesis on the size of the degeneracy set. Some of the properties
used during the proofs lead us to introduce a notion of intermediate Picard
hyperbolicity, which we last discuss.
