We present a decentralized nonlinear flow control scheme for a class of communication networks with physical constraints. Through a detailed analysis, we demonstrate that nonlinear system theory can be applied to cope with saturation nonlinearity and unknown disturbances in network flow control problems. We solve the constrained queue regulation problem against traffic interferences with control input and state saturation, under two explicitly identified conditions, namely a "PE" condition and a Lipschitz-like condition. Asymptotic regulation is achieved for both a single-node system and large-scale networks, for all feasible initial states. The trade-offs of various control parameter settings are revealed through our analysis. Computer simulations confirm the effectiveness of our non-linear network flow control scheme.