A novel technique is proposed for measurement of the group delay (GD) and the differential group delay (DGD) of optical material, components, and fiber. This new method is based on continuous polarization modulation of the stimulus optical field as opposed to sequential polarization state switching used in the traditional phase shift method. A new complete derivation of the phase shift method, based on the modified Jones calculus of elementary matrices, is presented. The derivation reveals that the phase shift measurement actually depends on all eight elementary parameters that represent DGD and optical frequency derivatives of polarization-dependent loss (PDL). Thus, the new expression for the phase shift includes the combined effect of PDL and DGD. The proposed method is evaluated by measuring a section of polarization-maintaining fiber and a 50 km length of single-mode fiber over a wavelength range from 1530 to 1610 nm. Measurements of DGD in a long single-mode fiber are shown to be highly insensitive to environmentally induced GD drift.