In this paper, we consider an exponentially dominant order .alpha. of a problem, and the matrix A is replaced by this number .alpha. in the above function. In Section 1, the Runge-Kutta method and the multistep methods generalized by this function. when the exponentially dominat order is positive, its numerical solutions can be accurately computed by these generalized methods. In Section 2, A- and B-stability of the generalized Runge-Kutta methods are tested. finally, in Section 3, a concept of AB-stability is introduced. And we study some sufficient conditions under which the generalized runge-kutta methods are AB-stable