Given a compact symplectic manifold $(M,\,\kappa)$,
$H^{2}(M,\,{\Bbb{R}})$\, represents, in a natural sense, the tangent space
of the moduli space of germs of deformations of the symplectic structure.
In the case $(M,\,\kappa,\,J)$ is a compact Kähler manifold, the author
provides a complete description of the subset of $H^{2}(M,\,{\Bbb{R}})$
corresponding to Kähler deformations, including the non-generic case,
where (at least locally) some hyperkähler manifold factors out from $M$.
Several examples are also discussed.