  We prove the Mirror Conjecture for Calabi-Yau manifolds equipped with a
holomorphic symplectic form. Such manifolda are also known as complex manifolds
of hyperkaehler type. We obtain that a complex manifold of hyperkaehler type is
Mirror dual to itself. The Mirror Conjecture is stated (following Kontsevich,
ICM talk) as the equivalence of certain algebraic structures related to
variations of Hodge structures. We compute the canonical flat coordinates on
the moduli space of Calabi-Yau manifolds of hyperkaehler type, introduced to
Mirror Symmetry by Bershadsky, Cecotti, Ooguri and Vafa.
