Numerical methods are investigated for solving a system of continuity equations that contain linear and nonlinear chemistry as source and sink terms. It is shown that implicit, finite-difference approximations, when applied to the chemical kinetic terms, yield accurate results when the equations are linear, but give poor results when the equations are nonlinear. In fact, when the equations are nonlinear, the implicit finite-difference scheme will be unstable if delta t is large. It is shown that for urban and larger scale air quality simulation models, the advection and chemical terms are more accurate than implicit treatments of the chemistry.