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A new notion of a dual Poisson-presymplectic pair is introduced and itsproperties are examined. The procedure of Dirac reduction of Poisson operatorsonto submanifolds proposed by Dirac is in this paper embedded in a geometricprocedure of reduction of dual Poisson-presymplectic pairs. The methodpresented generalizes those used by Marsden and Ratiu for reductions of Poissonmanifolds. Two examples are given.Comment: to appear in Journal of Physics A: Mathematical and Genera

Dirac reduction of dual Poisson–presymplectic pairs