We propose two algorithms for Q-learning that use the two-timescale stochastic approximation methodology. The first of these updates Q-values of all feasible state-action pairs at each instant while the second updates Q-values of states with actions chosen according to the 'current' randomized policy updates. A proof of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms on an application of routing in communication networks are presented on a few different settings. (c) 2007 Elsevier Ltd. All rights reserved.