In this paper we shall present some new results obtained from an application of Positive System Theory  to the problem of designing combined routing and flow control strategies for data communication networks. This application permits treating the combined routing and flow control problem in the framework of system stabilization and results in a hierarchical control scheme. The overall control effort consists of a distributed computation of a set of routing parameters at the lower level of network nodes and a computation on a slower time-scale of a set of combined parameters by a Supervisor (Network Control Center) at a higher hierarchical level. Specific algorithms are presented for adaptive updating of these parameters in order to realize improved network performance taking into account multiple objectives of end-to-end delay, throughput and nodal buffer management. The combined routing and flow control problem is attaining a great deal of importance in the recent times. This is due to the fact that the routing schemes and the flow control schemes implemented in existing data networks are designed independent of each other, where-as it has recently been determined [2,3] that a high degree of interplay exists between the two forms of control which has to be taken into account for realizing improved network performance. It has also been determined that a hierarchical control structure provides a very useful mechanism for an integration of routing and flow control [4,5].