  We study orthogonal and symplectic matrix models with polynomial potentials
and multi interval supports of the equilibrium measure. For these models we
find the bounds (similar to the case of hermitian matrix models) for the rate
of convergence of linear eigenvalue statistics and for the variance of linear
eigenvalue statistics and find the logarithms of partition functions up to the
order O(1). We prove also universality of local eigenvalue statistics in the
bulk.
