Molecular photoelectrons have been observed to be spin polarized even if ejected from a beam of randomly oriented molecules by unpolarized radiation. The polarization and the asymmetry parameter [Beta] for Br2, I2, CH3Br, and CH3I are compared with general predictions of a nonrelativistic model. While all available data of the differential cross section agree with this prediction, spin-polarization results partly disagree, manifesting the influence of the spin-orbit interaction upon the phases of molecular continuum wave functions.