  We study a properly convex real projective manifold with (possibly empty)
compact, strictly convex boundary, and which consists of a compact part plus
finitely many convex ends. We extend a theorem of Koszul which asserts that for
a compact manifold without boundary the holonomies of properly convex
structures form an open subset of the representation variety. We also give a
relative version for non-compact (G,X)-manifolds of the openess of their
holonomies.
