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Classical results show under suitable conditions that the sequence of non-Markovian processes $(X^n)_{n\\in\\mathbb{N}}$ converges to a Markov process and give its infinitesimal characteristics. Here, we consider a general sequence $(Z^n)_{n\\in\\mathbb{N}}$. Using a general result on stochastic averaging from [Kur92], we derive conditions which ensure that the sequence $(X^n)_{n\\in\\mathbb{N}}$ converges as in the classical case. 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