Abstract. In this talk, based on our earlier work, we propose a systematic method for symbolically computing the Lyapunov characteristic exponents, briefly LCE, of n-dimensional dynamical systems. First, we analyze in mathematics the LCE of n-dimensional dynamical systems. In particular, as an example, we discuss the LCE of the Lorenz systems. Then, to do the above task, a framework on representation and manipulation of a class of non-algebraic objects using non-standard analysis is established. In this framework, an algorithm can be developed for deriving some unknown relations on some objects involving limit processes. Finally, applying this algorithm to n-dimensional dynamical systems, we can show that their maximal LCE can be derived mechanically; particularly, for the Lorenz systems, we obtain an important result on the maximal LCE of the chaotic attractors of these systems - their dependence on the systems parameters.