We consider here the A + B --> 0 reaction between particles that diffuse, interact through short-range forces, and react on contact. In a plausible approximation the reaction can be described through a nonlinear diffusion equation, from which the scaling behavior of the respective A and B concentrations follows. We focus here on steady particle generation and obtain the exponents that govern the concentration’s growth. Through explicit Monte Carlo simulations of the underlying stochastic process we obtain directly these exponents; furthermore we show that the assumption of particle segregation in clusters is correct, by computing the correlation length.