We here theoretically outline and experimentally demonstrate that polarization spectroscopy can be combined with cavity ring down (CRD) spectroscopy, thereby retaining the specific advantages of both techniques. The b(1) Sigma(g)(+)(v'= 2) <--X-3 Sigma(g)(-)(v'' = 0) transition of molecular oxygen around 628 nm is used to demonstrate the possibility to selectively measure either the polarization-dependent absorption or the resonant magneto-optical rotation of gas-phase molecules in the appropriate setup. Just as in CRD absorption spectroscopy, where the rate of absorption is measured, in the here presented polarization-dependent CRD (PDCRD) detection scheme the rate of polarization rotation is measured, which enables the polarization rotation to be quantitatively determined. Apart from studying electro-optic and magneto-optic phenomena on gas-phase species, the PDCRD detection scheme is demonstrated to be applicable to the study of magneto-optical rotation in transparent solid samples as well. (C) 1997 American Institute of Physics.