We consider the Gause-type predator-prey system with a large class of growth and response functions, in the case where the response function is not smooth at the origin. We discuss the conditions under which this system has exactly one stable limit cycle or has a positive stable equilibrium point and we describe the basin of attraction of the stable limit cycle and the stable equilibrium point, respectively. Our results correct previous results of the existing literature obtained for the Holling response function x p /(a + x p), in the case where 0 < p < 1.