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We consider two-sorted algebras of pomsets (isomorphism classes of labeled partial orders) equipped with the operations of series and parallel product and series and parallel omega power. The main results show that these algebras possess a non-finitely based polynomial time decidable equational theory, which can be axiomatized by an infinite set of simple equations. Along the way of proving these results, we show that the free algebras in the corresponding variety can be described by generalized series-parallel pomsets. We also provide a graph theoretic characterization of the generalized series-parallel pomsets.