This volume contains the papers presented at the 8th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2005) and the 9th International Workshop on Randomization and Computation(RANDOM2005),whichtookplaceconcurrentlyattheUniversity of California in Berkeley, on August 22-24, 2005. APPROX focuses on algori- mic and complexity issues surrounding the development of e?cient approximate solutions to computationally hard problems, and APPROX 2005 was the eighth in the series after Aalborg (1998), Berkeley (1999), Saarbru ..cken (2000), Ber- ley (2001),Rome (2002),Princeton(2003),and Cambridge(2004).RANDOM is concerned with applications of randomness to computational and combinatorial problems, and RANDOM 2005 was the ninth workshop in the series foll- ing Bologna (1997), Barcelona (1998), Berkeley(1999), Geneva (2000), Berkeley (2001), Harvard (2002), Princeton (2003), and Cambridge (2004). Topics of interest for APPROX and RANDOM are: design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network designandrouting,packingand covering,scheduling,designandanalysisofr- domized algorithms, randomized complexity theory, pseudorandomness and - randomization,random combinatorialstructures, randomwalks/Markovchains, expander graphs and randomness extractors, probabilistic proof systems, r- dom projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of - proximation and randomness. The volume contains 20 contributed papers selected by the APPROX P- gram Committee out of 50 submissions, and 21 contributed papers selected by the RANDOM Program Committee out of 51 submissions.