We establish the existence of solutions for a nonlinear Volterra integral inclusion, involving a nonconvex valued orientor field and defined in a separable Banach space. Next we consider a random version of it and prove the existence of random solutions. Finally we examine a perturbed version of the original inclusion, with the pertubation being multivalued. Our results extend earlier ones by Chuong, Ragimkhanov, Lyapin, Milton-Tsokos, Papageorgiou amd Tsokos.