Discrete systems related to some equations of the Painleve-Gambier classification

We derive integrable discrete systems which are contiguity relations of two equations in the Painleve-Gambier classification depending on some paramet er. These studies extend earlier work where the contiguity relations for th e six transcendental Painleve equations were obtained. In the case of the G ambler equation we give the contiguity relations for both the continuous an d the discrete system. (C) 2000 Published by Elsevier Science B.V. All righ ts reserved.