We study the issue of asymptotic stability of a family of rate control algorithms with communication delays between network elements and extend our earlier results: First, we derive delay-dependent stability conditions with a family of well-known utility and resource price functions when a finite upper bound is known on the feedback delay. These conditions are shown to be consistent with known stability conditions in two extreme cases-no delay or an arbitrarily large delay. Secondly, we provide a lower bound on the convergence rate with the same utility and resource price functions when delay-independent stability conditions hold.