Theoretically and experimentally, the polarization eigenstates in a passive optical resonator with two partial polarizers are shown to be linear. Next to the resonator mirrors, the eigenvectors are orthogonal; between the two partial polarizers they are, in general, not orthogonal. This deviation from orthogonality may explain the observed elliptical polarization of the output of He-Ne lasers with skewed Brewster windows. The result of calculations are shown for the case of a resonator with two equal partial polarizers, each consisting of a plane parallel plate of glass oriented at the Brewster angle and for the case of two different partial polarizers consisting of one and two Brewster plates respectively. The directions of the eigenpolarizations and the deviation from orthogonality between the polarizers were computed as functions of the skew angle between the polarization axes of the partial polarizers. Within the experimental accuracy, the measured results agree with the theoretical predictions.