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The universal source coding theorem for stationary sources states that, by using a preselected code with sufficiently large block length, any stationary source can be encoded arbitrarily close to the optimum performance theoretically attainable for the source. The code construction typically used to prove this theorem offers no performance guarantees for nonstationary sources. A code construction (based on composition classes) is described which is shown to be universal for stationary sources. In addition, this code construction guarantees that the distortion for any block in the sequence will not exceed a maximum value determined by its composition.