We studied the dynamical critical behavior of a recently proposed competitive reaction model between monomers on a catalytic surface [E. C. da Costa and W. Figueiredo, J. Chem. Phys. 117, 331 (2002)]. The surface is represented by a square lattice and we consider the following reactions: A + A(B)-->A(2)(AB) where A and B are two monomers that arrive at surface with probabilities y(A) and y(B) = 1-y(A), respectively. The model is studied in the adsorption controlled limit by an epidemic analysis, where the initial condition is close to the absorbing state. We have determined the dynamic critical exponents of the model, which are related to the asymptotic behavior of the survival probability, number of empty sites (the order parameter) and mean square displacement from origin. These exponents agree with that of the directed percolation. (C) 2003 American Institute of Physics.