Drain-current transients of GaAs MESFETs are simulated in the range from 10-13 to 102 sec. The currents become constant temporarily at around t = 10-11 sec, but begin to decrease or increase after some periods, reaching real steady-state values. The slow transients are attributed to trapping and detrapping by deep levels in the substrate. Effects of introducing a p-buffer layer on drain-current drifts and small-signal parameters are also studied. It is concluded that the use of a low trap-density substrate combined with introducing a p-buffer layer is effective to utilize high-speed and high-frequency performances of GaAs MESFETs.