Two algorithms for the determination of the necessary limit of local error for the numerical solution of ordinary differential equation (ODE) systems describing homogeneous chemical and biochemical processes, and for the evaluation of their stiffness are developed. The approach for finding the necessary limit of local error of a numerical ODE solver is justified by the proof of the corresponding theorems. The application of the new algorithms implemented in version 2.1 of KinFitSim software to the simulation of real chemical systems is considered on the example of Belousov-Zhabotinsky reaction.