Abstract
Let be an irreducible Hermitian symmetric space of compact type with standard homogeneous complex structure. Then the real symplectic manifold has the natural complex structure . All -invariant Kéhler structures on -invariant subdomains of anticommuting with are constructed. Each hypercomplex structure of this kind, equipped with a suitable metric, defines a hyperkéhler structure. As an application, a new proof of the theorem of Harish-Chandra and Moore for Hermitian symmetric spaces is obtained.