The provision of Quality of Service (QoS) in Grid environments is still an open issue that needs attention from the research community. One way of contributing to the provision of QoS in Grids is by performing meta-scheduling of jobs in advance, that is, jobs are scheduled some time before they are actually executed. Therefore, it becomes more likely that the appropriate resources are available to run the job when needed, so that QoS requirements of jobs are met (i.e., jobs are finished within a deadline). This thesis presents a framework built on top of Globus and the GridWay meta-scheduler to provide QoS by means of performing meta-scheduling in advance decisions. This framework manages idle/busy periods of resources in order to choose the most suitable resource for each job by means of predictions techniques. As no prior knowledge on the duration of jobs is required by the users and to take into account the dynamism of this type of environments, some prediction techniques are presented to estimate the future status of resources (network inclusive) as well as the duration of jobs into them based on that information.