Two linear feedback control algorithms for handling and preventing congestion in broadband asynchronous transfer mode networks are proposed and analyzed. The fluid approximation model is described with a continuous-time system of delay-differential equations. The algorithms are asymptotically stable, and the transient processes are nonoscillatory. The control parameters are locally optimal (optimality is based on the asymptotic rate of convergence). The results of numerical experiments suggest that these parameters are globally optimal as well.