  We study the deformations of a holomorphic symplectic manifold $M$, not
necessarily compact, over a formal ring. We show (under some additional, but
mild, assumptions on $M$) that the coarse deformation space exists and is
smooth, finite-dimensional and naturally embedded into $H^2(M)$. For a
holomorphic symplectic manifold $M$ which satisfies $H^1(M,{\cal O}_M) =
H^2(M,{\cal O}_M)=0$, the coarse moduli of formal deformations is isomorphic to
$\Spec\C[[t_1, ..., t_n]]$, where $t_1$, ... $t_n$ are coordinates in $H^2(M)$.
  This revised version contains one minor improvement: exposition in Subsection
5.1 has been made more detailed and rigourous.
