Let $G/K$ be an irreducible Hermitian symmetric space of noncompact type. We study a $G$- invariant system of differential operators on $G/K$ called the Hua system. It was proved by K. Johnson and A. Korányi that if $G/K$ is a Hermitian symmetric space of tube type, then the space of Poisson-Szegö integrals is precisely the space of zeros of the Hua system. N. Berline and M. Vergne raised the question about the nature of the common solutions of the Hua system for Hermitian symmetric spaces of nontube type. In...