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This work proposes a parallel memetic algorithm applied to the total tardiness single machine scheduling problem. Classical models of parallel evolutionary algorithms and the general structure of memetic algorithms are discussed. The classical model of global parallel genetic algorithm was used to model the global parallel memetic analogue where the parallelization is only applied to the individual optimization phase of the algorithm. Computational tests show the efficiency of the parallel approach when compared to the sequential version. A set of eight instances, with sizes ranging from 56 up to 323 jobs and with known optimal solutions, is used for the comparisons.