[en] The kinetics of an irreversible dimer-trimer reaction of the type 2 A/sub 3/ +3 B/sub 2/ -- 6 AB by considering the precursor motion of the dimer (B/sub 2) on a square, as well as on a hexagonal surface, by using a Monte Carlo simulation have been studied. When the movement of precursors is limited to the first nearest neighborhood, the model gives reactive window widths of the order of 0.22 and 0.29 for the square and the hexagonal lattices, respectively, which are quite large compared to those predicted by the LH model. In our model, the reactive window width for a square lattice increases significantly as compared to that for the LH models of the same system on square and hexagonal lattices. The width of the reactive region increases when the precursor motion is extended to the second and the third nearest neighborhood. The continuous transition disappears when the precursor motion is extended to the third nearest neighborhood. The diffusion of B atoms does not change the situation qualitatively for both the precursor and the LH models. However, desorption of the dimer changes the situation significantly; i.e., the width of the reactive window shows an exponential growth with respect to the desorption probability of the dimer for both the precursor and the LH models. In our opinion, the inclusion of precursors in the LH model of the dimer-trimer reactions leads to a better and more realistic description of the heterogeneous catalytic reactions. Consequently, further numerical and theoretical activity in this field will be very useful for understanding complex heterogeneous reactions. (orig./A.B.)