Contributions of renormalon singularities

On the basis of some simple examples the authors suggest a general method for discussing the contribution of renormalons to the Borel transform based on the general analytical structure of the renormalization group β function. No simple principal value or contour integral Borel representation seems to be possible. Instead a splitting of the Borel transform at each renormalon singularity seems to be necessary making the infinite sum over renormalons possibly difficult to define. (Auth.)