We consider solutions for distributed multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We show first distributed solutions that allow (1 + ε) approximation and whose convergence time is essentially linear in the maximal path length, and is independent of the number of commodities and the size of the graph. Our algorithms use a very natural approximate steepest descent framework, combined with a blocking flow technique to speed up the convergence in distributed and parallel environment. Previously known solutions that achieved comparable convergence time and approximation ratio required exponential computational and space overhead per agent. © 2012 ACM.