[en] The combination of the present fragment separator FRS and the cooler-storage ring ESR at GSI provides conditions for accurate mass and unique half-life measurements of exotic nuclei. A major part of this doctoral work has been devoted to investigations of the isochronous ion-optical operating mode of the present ESR facility and the planned Collector Ring (CR) facility at FAIR. A detailed ion-optical study of the isochronous storage ring with the emphasis on the main parameters has been done. For example, a simple scaling law providing a quantitative estimate for the mass resolving power as a function of the transverse acceptance has been derived. The ion-optical matching of the FRS-ESR has been calculated and experimentally verified for both the standard and the isochronous operating modes of the ESR. In addition, the dispersion function of a stored ion beam has been measured for both ion-optical modes at the straight section. The improved setting for higher transmission in the standard mode has been used in an experiment on the half-life measurements of highly-charged ions. Orbital electron capture (EC) and/or β⁺-decay rates of ¹⁴⁰Pr ions with zero-, one- and two- bound electrons have been measured. A complementary future study of EC-decay in highly-charged ⁶⁴Cu ions is discussed. Based on the present experience, the ion-optical matching between the future in-flight fragment separator Super-FRS and the CR has been calculated. The isochronous mode of the CR has been calculated. A dedicated Monte-Carlo code (ISOCHRON) has been developed in order to investigate the influence of the transverse acceptance, the closed orbit distortions, the fringe fields of the quadrupoles, the magnetic field imperfections of the magnets on the mass resolving power. The influence of chromaticity on the isochronicity has been investigated. The correction of the chromaticity and of second-order isochronicity has been performed employing sextupole magnets in the arcs of the CR. The influence of nonlinear field errors and the third-order isochronicity are corrected with additional sextupole and octupole fields. (orig.)