AbstractA class of Runge‐Kutta‐Rosenbrock methods is discussed for the numerical solution of the initial value problem for stiff systems of ordinary differential equations. We pay special attention to the use of time‐lagged Jacobian matrices. The aim is to obtain an appreciable reduction in the number of Jacobian matrix evaluations and related matrix factorizations. When dealing with large systems the costs of these computations normally form a large proportion of the total integration costs of the Rosenbrock m