Abstract. Let X = G/K be a semisimple symmetric space of noncompact type. A horosphere in X is an orbit of a maximal unipotent subgroup of G. The set Hor X of all horospheres is a homogeneous space of G. The horospherical Radom transform suggested by I. M. Gelfand and M. I. Graev in 1959 takes any function ϕ on X to a function on Hor X obtained by integrating ϕ over horospheres. We explicitly describe the dual transform in terms of its action on polynomial functions on Hor X
