Starting from the vectorial Rayleigh-Sommerfeld integrals, the free-space propagation expressions for vectorial Hermite-Laguerre-Gaussian (HLG) beams beyond the paraxial approximation are derived. The far-field expressions and the scalar paraxial results are given as special cases of our general expressions. The intensity distributions of vectorial nonparaxial HLG beams are studied and illustrated with numerical examples.