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The pointwise multiplication on a full tribe and the product operation on an MValgebra play a crucial role in the construction of a joint observable. In the present paper we introduce a quasi product operation on Boolean D-posets and describe its properties. Our quasi product generalizes product on MV-algebras and in some cases also t-norms.Keywords Boolean D-poset · MV-algebra · Quasi product · t-norm 1 Basic notions D-posets [14] and, equivalently, effect algebras [10] generalize various classical algebraic structures modeling quantum mechanics and the fuzzy sets theory systems. The two structures are based on different approaches. The primary operation on effect algebras is a sum and the primary operation on D-posets is a difference of two comparable elements.A D-poset is a partially ordered set P , with a greatest element 1 and a smallest element 0, on which a partial binary operation difference b a is defined if and only if a ≤ b; it fulfills the following conditions:In every D-poset P the following three statements are equivalent [13]:(c1) For every two elements a and b from P there exist c, d ∈ P such that d ≤ a ≤ c, d ≤ b ≤ c and c a = b d;