The holonomy group G of a pseudo-quaternionic-Kählerian manifold of signature (4r, 4s) with non-zero scalar curvature is contained in Sp(1) · Sp(r, s) and it contains Sp(1). It is proved that either G is irreducible, or s = r and G preserves an isotropic subspace of dimension 4r , in the last case, there are only two possibilities for the connected component of the identity of such G. This gives the classification of possible connected holonomy groups of pseudo-quaternionic-Kählerian manifolds of non-zero scalar curvature.

Possible holonomy algebras of pseudo-quaternionic-Kählerian manifolds of signature (4, 4) are classified. Using this, a new proof of the classification of simply connected pseudo-quaternionic-Kählerian symmetric spaces of signature (4, 4) is obtained.

The holonomy algebra of a pseudo-hyper-Kählerian manifold of signature (4, 4n + 4) is a subalgebra of sp(1, n + 1). Possible holonomy algebras of these manifolds are classified. Using this, a new proof of the classification of simply connected pseudo-hyper-Kählerian symmetric spaces of index 4 is obtained.

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