  In this paper we provide new conditions for the Malliavin differentiability
of solutions of Lipschitz or quadratic BSDEs. Our results rely on the
interpretation of the Malliavin derivative as a G{\^a}teaux derivative in the
directions of the Cameron-Martin space. Incidentally, we provide a new
formulation for the characterization of the Malliavin-Sobolev type spaces
$D^{1,p}$ .
