The surface reaction mechanism of Ga(CH3)(3) (trimethylgallium : TMG) on GaAs during monolayer growth by molecular layer epitaxy was investigated by quadrupole mass spectroscopy. The desorbed species by the reaction of TMG on GaAs (001), (111)As, and (111)Ga surfaces have been studied by the quadrupole mass spectroscopy signals. At 420-510 degrees C, adsorbed monolayers of GaCH3 are formed on the GaAs (001) surface by sufficient TMG introduction. The adsorbed GaCH3 form Ga and CH3 with a time constant of 15-36 s in the transient state. Furthermore, the decomposition of TMG occurs on this adsorbed GaCH3 or Ga layer as the steady state reaction progresses and volatile GaCH3, Ga(CH3)(2), and CH3 are produced. In the case of (111)As, TMG decomposed into Ga and CH3 above 480 degrees C, below which the volatile adsorbates GaCH3 and Ga(CH3)(2) are formed. These adsorbates migrate on the surface and react with each other or with TMG, gradually decomposing into Ga. TMG adsorbs temporarily on the (111)Ga surface and decomposes into GaCH3 and Ga(CH3)(2) and they desorb quickly; therefore no adsorbates stay on the (111)Ga surface after TMG injection. At temperatures below 450 degrees C, TMG adsorbs on the (111)Ga surface with no TMG decomposition.