  We study the class $\mathcal{K}_{2}+\mathcal{K}_{4}$ of homogeneous
pseudo-K\"ahler structures in the strongly degenerate case. The local form and
the holonomy of a pseudo-K\"ahler manifold admitting such a structure is
obtained, leading to a possible complex generalization of homogeneous plane
waves. The same question is tackled in the case of pseudo-hyper-K\"ahler and
pseudo-quaternion K\"ahler manifolds.
