Several nonlinear Internet congestion control schemes have been proposed in the previous years based on primal and dual decompositions of convex yet centralized optimization problems that describe the bandwidth allocation problem. This design methodology uses (sub) gradient methods for the design of node/link dynamics and guarantees nominal functionality for arbitrary system sizes. In this technical note we analyze the robustness of such nonlinear schemes to the presence of multiple, non-commensurate (heterogeneous) communication delays.