The method for the effective action for massive quantum fields in curved space-time is based on the conformal representation of the fields action and consequent integration of the conformal anomaly. As a relevant cosmological application, we find that if we take the masses of the fields into account, then the stable anomaly-induced inflation slows down due to the effect of massive fermions. In super symmetric theories this mechanism can be specially efficient, for it may naturally provide the graceful exit from the inflationary to the FLRW phase. Taking the SUSY breaking into account, the anomaly-induced inflation could be free of the well-known difficulties with the initial data and also with the amplitude of the gravitational waves. ©2002 Plenum Publishing Corporation.