Abstract: This paper is the continuation of [1]. In this paper, we give another criteria of the existence of solutions for nonlinear random Volterra integral. A comparison theorem and the existence of random extremal solutions are also obtained by using the notion of ordering with respect to a cone. Our theorems generalize the corresponding results of Vaughan [2,3]and Lakshmikantham[4,5].

Key words: moving belts, viscoelasticity, Lie group, dynamic response