CR geomagnetic cutoff rigidities in the magnetic field of two different empirical models of the magnetosphere—Tsyganenko 1989 (Ts89) and Tsyganenko 1996 (Ts96)—have been determined by the method of trajectory computations for two magnetic storms of January 23–31, 1985, and November 23–29, 1986, when anomalies were observed on the satellites and processing systems operated intermittently. A comparison of geo-magnetic cutoff rigidities in Ts89 and Ts96 models indicated that the difference between these rigidities during the above storms can reach 0.5 GV at midlatitude stations