Two experimental methods of measuring masses of exotic nuclei in the storage ring ESR are presented. Bismuth and nickel fragments were produced via projectile fragmentation, separated and investigated with the combination of the fragment separator FRS and the ESR: (i) Direct mass measurements of relativistic projectile fragments were performed using Schottky mass spectrometry (SMS), i.e., exotic nuclei were stored and cooled in the ESR. Applying electron cooling, the relative velocity spread of circulating low intensity beams can be reduced below 10⁻⁶. Under this condition a mass resolving power of up to m/Δm=6.5·10⁵ (FWHM) was achieved in a recent measurement. Previously unknown masses of more than 100 neutron-deficient isotopes have been measured in the range of 60≤Z≤84. Using known Q_α values the area of known masses could be extended to more exotic nuclei and to higher proton numbers. The results are compared with mass models and extrapolations of experimental values. In a second experiment with ²⁰⁹Bi projectiles the area of the measured masses was extended to lower proton numbers. Due to various improvements at the ESR the precision of the measurements could be raised. (ii) Exotic nuclei with half-lives shorter than the time needed for SMS (present limit: T_1/2 ≈ 5 sec) can be investigated by time-of-flight measurements whereby the ESR is operated in the isochronous mode. This novel experimental technique has been successfully applied in first measurements with nickel and neon fragments where a mass resolving power of m/Δm=1.5·10⁵ (FWHM) was achieved.