A method of stabilizing chlorofluorocarbon compositions thereby is provided. The stabilized composition comprises a chlorofluorocarbon and a sufficient amount of an epoxidized, generally high molecular weight stabilizer having an oxirane content sufficient to effectively stabilize the chlorofluorocarbon. The stabilizer is preferably an epoxidized oil having a molecular weight in the range of about 300 to about 1,500 and an oxirane content of at least about 4 %. The method includes the step of adding a sufficient amount of such a stabilizer to the chlorofluorocarbon composition. The chlorofluorocarbon composition typically comprises chlorofluoromethane, chlorofluoroethane, mixtures thereof or a chlorofluorocarbon-alcohol azeotropic solution. Also provided is an improved continuous dialyzer cleaning method utilizing the stabilized chlorofluorocarbon composition.