Off-critical perturbations of two-dimensional rational conformal field theories given by scalar primary operators with scaling dimensions smaller than (1/2, 1/2) are considered. The Gell-Mann-Low expansion is shown to converge in finite volume. (orig.)This paper supersedes the preprint BONN-HE--93-03SIGLEAvailable from TIB Hannover: RN 5063(93-48) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman