Periodic comet Perrine-Mrkos was observed during its three consecutive returns during 1955, 1961/62, 1968/69, and since that time it has never been seen. Probably large nongravitational effects quickly changing with time did not allow to make an exact prediction of the future comet's returns. We used 66 astrometric observations of the comet from 1955-1969 to improve the comet's orbits and to determine values of nongravitational parameters. We applied the method based on the rotating and precessing cometary nucleus with a forced precession to determine seven nongravitational parameters. Thus, we found satisfactory solution linking well the last three apparitions with the rms residual equal to 1''.90. The solution gives a very good fit to the earlier observed perihelion passages of the comet in 1909 and in 1896. Therefore, we were able to make prediction of the comet's return in 2002 and we calculated the search ephemeris.
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