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The stable version of the anomaly-induced inflation does not need a finetuning and leads to sufficient expansion of the Universe. The non-stableversion (Starobinsky model) provides the graceful exit to the FRW phase. Weindicate the possibility of the inflation which is stable at the beginning andunstable at the end. The effect is due to the soft supersymmetry breaking andthe decoupling of the massive sparticles at low energy.Comment: 10 pages, 2 figures using axodraw. Modified version. Discussion  concerning the gravitational scale modified, the effect of massive particles  in the last stage of inflation taken into accoun

THE GRACEFUL EXIT FROM THE ANOMALY-INDUCED INFLATION: SUPERSYMMETRY AS A KEY