In this paper, we investigate how congestion control can achieve efficient usage of network resources in the presence of heterogeneous communication delays between network users and resources. To this end, we consider a fluid flow model of network behavior. We study the stability of the system's behavior under small perturbations around the target equilibrium point (local stability). We establish several criteria for stability of certain linear delay-differential equations, via a technique which essentially reduces the question to studying stability of ordinary differential equations. These results are then used to derive sufficient conditions for local stability of the network congestion control problem. The same issue has been studied in [9], where the authors propose a conjecture according to which local stability can be ensured in a distributed way. The correctness of the conjecture is established in [9], only in degenerate cases where feedback delays coincide. Our results show that a modified form of the conjecture holds true for arbitrary feedback delays.