Software for the simulation of dynamic operation and adaptive control of combined systems of monolithic catalytic reactors and adsorbers (catalytic traps) for treatment of exhausts from mobile sources is described. Monolithic reactors are modelled by a spatially I-D two-phase model consisting of a system of PDE's (axial heat dispersion included! and for the adsorbers a spatially I-D model (pseudohomogeneous for the enthalpy balance) is used. The system of PDE's is solved by the combination of the Crank-Nicolson method (reactors) and by the method of lines (adsorbers). Results of the application of the software to two examples - the use of adsorber-reactor systems with mutual heat exchange for the solution of the 'cold-start' problem and an adaptive dynamically operated system of coupled monoliths for NOx reduction using feed-forward neural network for predictive control are discussed in detail.