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Malt’tsev–Neumann products of semi-simple classes of associative rings are studied and some conditions which ensure that such a product is again a semi-simple class are obtained. It is shown that both products, ${𝒮}_1\circ {𝒮}_2$ and ${𝒮}_2\circ {𝒮}_1$ of semi-simple classes ${𝒮}_1$ and ${𝒮}_2$ are semi-simple classes if and only if they are equal.