Orthogonal Polynomials for a Family of Product Weight Functions on the Spheres Based on the theory of spherical harmonics for measures invariant under a finite reflection group developed by Dunkl recently, we study orthogonal polynomials with respect to the weight functions $|x_1|^{\alpha_1}\cdots |x_d|^{\alpha_d}$ on the unit sphere $S^{d-1}$ in $\RR^d$. The results include explicit formulae for orthonormal polynomials, reproducing and Poisson kernel, as well as intertwining operator. Keywords:Orthogonal polynomials in several variables, sphere, h-harmonicsCategories:33C50, 33C45, 42C10