It is shown that the substrate current in GaAs MESFET\´s may be related to the electron injection into the substrate region adjacent to the high-field domain in the active layer. A simple one-dimensional calculation shows that the substrate current I
subis proportional to 

 and 

 where V
dsis the drain-to-source voltage, n
0is the doping density in the active layer. At 

 cm
-3and 

 V we estimate 

 mA per millimeter gate in good agreement with experimental results.