Abstract-Grids provide secure, utility-like access to a wide variety of large-scale, distributed computational and storage resources. In particular, the European Grid Infrastructure (EGI) and Open Science Grid (OSG) have excelled in processing vast workloads of independent jobs for the research community.Researchers demand increasingly faster processing speeds to solve increasingly larger and more complex problems. To meet this need, attention has shifted over the past decade away from single-core processing models towards the use of multi-core, many-core and massively parallel computational accelerators. The increasing availability and use of General Purpose Graphic Processing Units (GPGPUs) are an example of this.This paper addresses many of the challenges that exist in the integration of resources such as GPGPUs into Grid infrastructures. Specifically, solutions are proposed for discovering and describing GPGPU Grid resources, specifying multi-GPGPU job requirements, performing multi-GPGPU allocation to jobs, dynamically updating publicly-readable GPGPU usage information and enforcing GPGPU access control to prevent distinct jobs from inadvertently accessing the same device. The proposed solution is fully compatible with widely-used and accepted standards and middleware including the GLUE 2.0 schema and EGI Unified Middleware Distribution. A prototype implementation is also described.