Dynamic inter-domain collaborations and resource sharing comprise two key characteristics of mobile Grid systems. However, inter-domain collaborations have proven to be vulnerable to conflicts that can lead to privilege escalation. These conflicts are detectable in inter-operation policies, and occur due to cross-domain role relationships. In addition, resource sharing requires to be enhanced with resource usage management in virtual organizations where mobile nodes act as resource providers. In this case the enforcement of resource usage policies and quality of service policies are required to be supported due to the limited capabilities of the devices. Yet, the ANSI INCITS 359-2004 standard RBAC model provides neither any policy conflict resolution mechanism among domains, nor any resource usage management functionality. In this paper, we propose the domRBAC model for access control in mobile Grid systems at a low administrative overhead. The domRBAC is defined as an extension of the standardized RBAC by incorporating additional functionality to cope with requirements posed by the aforementioned systems. As a result, domRBAC facilitates collaborations among domains under secure inter-operation, and provides support for resource usage management in the context of multi-domain computing environments, where mobile nodes operate as first-class entities.