In this paper one gives the decomposition of the space of tensors which have the symmetries of the covariant curvature tensor of a torsionless symplectic connection into Sp(n)-irreducible components. This leads to three classes of symplectic connections: flat, Ricci flat and reducible (i.e., with an expression like for Kähler manifolds of constant holomorphic sectional curvature). These cases are discussed for the canonical symplectic connection of a pair of transversal polarizations, where corresponding characteristic properties are given. In the reducible case, the Pontrjagin classes of the manifold are computed. If the pair of polarizations is real, and it has singularities, the Lehmann residues are considered [\textit{D. Lehmann}, Ann. Inst. Fourier 31, No.1, 83-98 (1981; Zbl 0432.57007)].