Future Grid Networks should be able to provide Quality of Service (QoS) guarantees to their users. In this work we propose a framework for Grid Networks that provides deterministic delay guarantees to its Guaranteed Service (GS) users and best effort service to its Best Effort (BE) users. The proposed framework is theoretically and experimentally analyzed. We also define four types of computational resources based on the type of users (GS, BE) these resources serve and the priority they give them. We implement the proposed QoS framework for Grids and verify that it not only satisfies the delay guarantees given to GS users, but also improves performance in terms of deadlines missed and resource use. In our simulations, data from a real Grid Network are used, validating in this way the appropriateness and usefulness of the proposed framework.