We have recently reported the optical detection of electric two-level system (TLS) dipoles in an organic polymer glass (Phys. Rev. Lett. 1995, 74, 5252). Here we present the results of more detailed investigations of electric properties of TLS in two-polymer glasses and a model description of the action of the external electric field. The influence of an external electric field on spectral diffusion (SD) in optical spectra of chromophores in organic amorphous solids at temperatures of 50-700 mK has been discovered and investigated via persistent hole burning. The field-induced spectral diffusion is caused by the interaction of the electric dipole moments of TLS with an external field. Electric field cycles disturb the equilibrium of the TLS ensemble. This causes an additional reversible diffusional broadening of spectral holes. A model description of the effect is presented, which is in quantitative agreement with the experimental results. The average values of the electric dipole moments of the TLS in two glasses, polymethylmethacrylate and polystyrene, are found to be on the order of 0.2 and 0.1 D, respectively. A modification of the hole-burning technique, based on the measurement of field-induced SD, is proposed that permits an increase of the time resolution of SD experiments far below the duration of the burning process. The investigation of the field-induced SD as a function of the field cycle time in the region of 1-300 min yields a slowly decreasing value of the TLS dipole moment with increasing cycle time. This effect points to a correlation between the dipole moments and the relaxation rates of TLS, which, to our knowledge, has not been observed before.