Let τ be a hereditary torsion theory on ModR and suppose that Qτ:ModR → ModR is the localization functor. It is shown that for all R‐modules M, every higher derivation defined on M can be extended uniquely to a higher derivation defined on Qτ(M) if and only if τ is a higher differential torsion theory. It is also shown that if τ is a TTF theory and Cτ : M → M is the colocalization functor, then a higher derivation defined on M can be lifted uniquely to a higher derivation defined on Cτ(M).