We present results from two methods of direct mass mesurements of relativistic exotic nuclei stored in the storage ring ESR. Schottky Mass Spectrometry (SMS) with electron-cooled ions is well suited for long-lived nuclei (T_1/2 ≥ 10 s), and the Isochronous mass measurements (IMS) for hot fragments (T_1/2 ≥ 1 μs). In addition, SMS provides information on nuclear lifetime for bare and highly ionized atoms.