arXiv:solv-int/9901006v1 19 Jan 1999 The hunting for the discrete Painlev´e VI equation is over B. Grammaticos GMPIB , Universit´e Paris VII Tour 24-14, 5 e ´etage 75251 Paris, France A. Ramani CPT, Ecole Polytechnique CNRS, UMR 7644 91128 Palaiseau, France Abstract We present the discrete, q-, form of the Painlev´e VI equation written as a three-point mapping and analyse the structure of its singularities. This discrete equation goes over to P VI at the continuous limit and degenerates towards the discrete q-P V through coalescence. It possesses special solutions in terms of the q-hypergeometric function. It can bilinearised and, under the appropriate assumptions, ultradiscretised. A new discrete form for P V is also obtained which is of difference type, in contrast with the ‘standard’ form of the discrete P V . Finally, we present the ‘asymmetric’ form of q-P VI as a system of two first-order mappings involving seven arbitrary parameters.