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An analysis of the kinetics of stress relief annealing in amorphous alloys, with particular emphasis on the effect of annealing on the resulting magnetic properties, is made. Based on this analysis, an optimal procedure for annealing amorphous alloy magnetic cores is suggested. It involves a fast heatup to a high temperature for a short time. The expected benefits of this procedure are decreased embrittlement, lower strain induced anisotropy, and lower residual stresses. The conventional technique for stress relieving magnetic cores proved unsuitable for the application of the new annealing treatment. A new technique was devised in which the ribbon is dynamically annealed as it is wound onto the core. The magnetic properties of the resulting toroids are superior to those produced by the conventional technique.