This note considers the design of transmission control protocol (TCP)-like congestion control protocols for deployment in high-speed communication networks. A basic problem in this area is to design congestion control strategies that probe more aggressively than standard TCP, but which coexist with each other and result in globally stable and equitable network behavior. In this note, we take a first step towards this goal, by formulating the TCP dynamics as a discrete linear system with nonlinear feedback gain. Under the assumption of player synchronisation, conditions for global network stability are derived in the form of growth bounds on the local nonlinear probing functions.