The equivalence between theories depending on the derivatives of R, i.e. f (R, ∇R, ..., ∇ n R), and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is shown that f (R, ∇R, ..., ∇ n R) theories are equivalent to scalar-multi-tensorial ones resembling Brans-Dicke theories with kinetic terms ω0 = 0 and ω0 = − 3 2 for metric and Palatini formalisms respectively. This result is analogous to what happens for f (R) theories. It is worthy emphasizing that the scalar-multi-tensorial theories obtained here differ from Brans-Dicke ones due to the presence of multiple tensorial fields absent in the last. Furthermore, sufficient conditions are established for f (R, ∇R, ..., ∇ n R) theories to be written as scalar-multi-tensorial theories. Finally, some examples are studied and the comparison of f (R, ∇R, ..., ∇ n R) theories to f (R, R, ... n R) theories is performed.