Trimethylgallium (TMGa) is an important source gas for metal-organic chemical vapor deposition (MOCVD) and metal-organic molecular beam epitaxy (MOMBE). In the last three years, workers in three different laboratories have examined the pyrolysis of trimethylgallium (TMGa) on heated substrates. However, the mechanism of the decomposition process is still not understood. In this paper we consider the mechanism of the TMGa decomposition on a hot Si(100) substrate in a molecular beam system. It is found that at TMGa doses of 1×1015 molecules/cm2 or less, the decomposition process in the beam system is the same as that reported by Lee et al., Surface Sci. 216, 173 (1989) in studies where TMGa was dosed at low temperature and then the substrate was heated. However, at higher TMGa doses, the mechanism in the molecular beam system is different than the ones reported previously. It is possible to transiently populate a weakly bound state which we assign to TMGa adsorption in the second monolayer. If me sample is below 400 K, the TMGa in the second monolayer desorbs. However, at higher temperatures, the TMGa in the second monolayer can react to form a CHx group (x=3 or 4) and dimethylgallium. The dimethylgallium desorbs. However, some of the CHx groups remain bound to the substrate leading to extra carbon incorporation. There also is evidence for formation of traces of monomethylgallium above 500 K and an indication of methyl radical desorption above 650 K. Thus it seems that at high doses, the decomposition of TMGa on a hot substrate is somewhat different than the decomposition of a monolayer of TMGa which has been adsorbed at low temperatures and then heated. These results explain some of the apparent discrepancies in the literature.