This paper presents some results about bounds for coincidence indices of Nielsen coincidence classes for maps between nonorientable surfaces. Denoting by Kn the nonorientable surface constructed by a connected sum of n torus with a Klein bottle,the author proves: (i) for pairs of maps between two Klein bottles or for pairs of maps from a Klein bottle to a surface Kn the coincidence class index is bounded. (ii) for pairs of maps from Kn to the Klein bottle the coincidence class index is unbounded.Other boundedness results are given for more technical conditions, including one for self maps.