Abstract: In this paper we consider pairs of recurrence relations where we are interested in the ratio of the iterates rather that in the iterates per se. Such recurrences occur i.e. when evaluating continued fractions, orthogonal polynomials or the characteristic polynomial of a symmetric tridiagonal matrix. Although such recurrence relations are compact and straight-forward to evaluate, the function value and the derivative might overflow while the ratio may still be a reasonable machine number. We describe, in this paper, how to avoid overflow and derive a new recurrence relation which allows us to compute the ratio directly.