This book constitutes the thoroughly refereed post proceedings of the Second International Workshop on Approximation and Online Algorithms, WAOA 2004, held in Bergen, Norway in September 2004.The 21 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement from 47 submissions. WAOA is devoted to the design and analysis of algorithms for online and computationally hard problems. Among the topics addressed are applications to game theory, approximation classes, coloring and partitioning, competitive analysis, computational finance, cuts and connectivity, geometric computations, inapproximability results, mechanism design, network design, routing, packing and covering, paradigms, randomization techniques, and scheduling problems.