Аннотация:We discuss calculation of the Gell-Mann–Low function in supersymmetric theories with the higher covariant derivative regularization and find that all integrals, defining this function, are possibly integrals of total derivatives. For the contribution of matter superfields this is partially explained by substituting solutions of Slavnov–Taylor identities into the Schwinger–Dyson equations. We find that the exact Gell-Mann–Low function coincides with the Novikov, Shifman, Vainstein and Zakharov β-function only if there is an identity for Green functions, which does not follow from any known symmetry of a supersymmetrictheory.