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This paper presents the issue of capacity variable routing in Satellite-HAP system networks with multicasting capabilities, for different traffic types, with the objective of minimizing the short term traffic load oscillations and reacting to the long term changes of the traffic loads. This is realized by learning from the past and using it to influence the current decision. Some of the major QOS constraints (Delay and link Utilization) have been taken into account to meet the criteria of the advance multimedia applications. The proposed routing technique includes the joint utilization and delay metrics which allow the traffic load balancing between the satellite links and HAP links taking the advantage of both segments. The performance of the proposed routing techniques is evaluated using the appropriate simulation models, where the improved performance has been reflected in reducing the number of path re-routing by almost 50%.