The performance of a readout system for the Synchrotron Radiation Detector (SRD) is studied. The detector is proposed as part of the Alpha Magnetic Spectrometer experiment, an experiment to fly on the International Space Station (ISS) beginning of 2005. The SRD is designed to detect the synchrotron radiation from electrons and positrons (TeV energy range) produced in the earth's magnetic field. For the planned array of scintillators and photomultipliers a readout system is chosen, which is compact, space qualified and has a low-power consumption. The low-power chip APV, originally designed for the CMS experiment at LHC (CERN), is foreseen for the readout. To overcome the diffuse background from photons and charged particles the SRD readout must have a time resolution better than 10 ns. The intrinsic time resolution (sigma from Gauss fit) of the APV25-S0 was found to be 0:4670:01 and 0:6870:02 ns for the APVM, whereas the time resolution of the photomultiplier-APV readout system was measured to be 2:7370:10 ns for the APV25-S0 and 2:9070:21 ns for the APVM. The investigated timing capabilities of the photomultiplier-APV readout system show that the APV chip is suitable for the SRD readout.