Summary: A nonlinear multiscale technique is used to describe the time history of a spatially homogeneous chain-branching/chain-breaking explosion when chain branching is much faster than chain breaking. The authors select a two-step chemistry model that closely reproduces the ignition characteristics of hydrogen-oxygen systems above the second explosion limit. The resulting combustion history exhibits an induction period with small radical concentrations, followed by a short period of rapid radical growth and a long period of slow radical recombination. The solution can be described by using the ratio of the rate of chain breaking to that of chain branching as an asymptotically small parameter. The problem is formulated by identifying a linear combination of the original variables that evolves with the slow time of radical recombination, and by allowing the fast time to depend on this slowly varying unknown. The associated solution procedure is nonstandard in that it exhibits different solvability conditions for the slow time evolution in the induction and recombination periods. The method proposed emerges as a natural alternative to activation-energy asymptotics for the analysis of branched-chain explosions at high temperatures.