L. Vretare [Math. Scand. 39, 343–358 (1976; Zbl 0387.43009)] proved that the spherical functions on a Riemannian symmetric space of the compact type of rank \(l\) are orthogonal polynomials in \(l\) variables with respect to a certain positive weight function. In this thesis, this result is generalized to intertwining functions.