abstract: What we call a twisted Poisson kernel on the unit disc or on a bounded symmetric domain is a product of powers of the ordinary Poisson kernel and of the Szego kernel. The corresponding Poisson integrals are eigenfunctions of certain modified Laplace operators. They have recently been studied, for the classical domains, by K. Okamoto and his collaborators. Group theoretically they can be interpreted as Poisson transforms from line bundles on the Shilov boundary to line bundles on the domain. New results include a classification-free extension of those of Okamoto et al. to all symmetric domains and the formulation of Hua-type differential equations in the tube type case.