The epistemological problems of unification of two distinct theories are discussed. An approach related to the work of Soviet authors (Stepin, Podgoretzky and Smorodinsky) is used and developed. The notion of ‘crossbred objects’—theoretical objects with contradictory properties which are part of the domain of application of two independent theories—is introduced which helps to describe the dynamics of revolutionary theory change. The occurrence of the cross-contradiction of two theories is reconstructed and the reductionistic and the synthetic means of its elimination are (...) proposed. The results of the methodological analysis are applied to the paradox of equivalence. (shrink)