  The Time-of-Flight (TOF) system of the AMS detector gives the fast trigger to
the read out electronics and measures velocity, direction and charge of the
crossing particles. The first version of the detector (called AMS-01) has flown
in 1998 aboard of the shuttle Discovery for a 10 days test mission, and
collected about $10^8$ events. The new version (called AMS-02) will be
installed on the International Space Station and will operate for at least
three years, collecting roughly $10^{10}$ Cosmic Ray (CR) particles. The TOF
system of AMS-01 successfully operated during the test mission, obtaining a
time resolution of 120 ps for protons and better for other CR ions. The TOF
system of AMS-02 will be different due to the strong fringing magnetic field
and weight constraints
