A kinetic model for the transalkylation of methylamines over amorphous silica/alumina is presented. The experimental data obtained at temperatures ranging from 623 to 683 K and pressures ranging from 0.2 to 2 MPa were described adequately. Transalkylation reactions occur between ammonia/methylamine adsorbed on an acid site and ammonia/methylamine adsorbed on a neighboring base site. In all reaction paths, the surface reaction between adsorbed species was assumed to be rate determining. At all pressures, the fraction of free acid sites as calculated by the model is very low. The fraction of free base sites is low at high pressures only. Models derived from other mechanisms were rejected based on a statistical analysis, mechanistic considerations, and physicochemical interpretation of the parameters. An industrial transalkylation reactor was simulated. To enhance the rate of dimethylamine formation, a mixture with an excess of monomethylamine and a deficit of ammonia and trimethylamine is recommended as the inlet composition for a transalkylation reactor. Decreasing the inlet partial pressure of ammonia results in a reduced amount of catalyst required to obtain the equilibrium concentration of dimethylamine.