The Verdet constant (V), which governs magnetic optical rotation, has been evaluated, at several frequencies, as a quadratic response function for H2, N2, CO, and FH, in the random-phase approximation (RPA). At the same time, the ‘‘normal’’ Verdet constant (VN) has been found from the linear response function in both RPA and second-order polarization propagator approximations (SOPPA), though in the latter case only for a single frequency. For H2 and N2, V is in good agreement with experiment, and the ratio V/VN accords very well with other accurate results. For CO the effect of correlation turns out to be more important. For FH there are no other results for V with which we can compare; however, SOPPA calculations on the normal Verdet constant show a dramatic effect for electron correlation. It appears that V/VN (which in all cases is only slightly dependent on frequency) is close to unity for FH, thus ruling out a connection between this ratio and molecular polarity. Zero-point-vibrational averaging is taken into account in the calculations and the effect of shifting the origin of the gauge is discussed.