Let A be an algebra. A sequence d = {dn}∞ n=0 of linear operators on A is called a higher derivation if d0 is the identity mapping on A and dn(xy) = Pn k=0 dk(x)dn−k(y), for each n = 0, 1, 2, . . . and x, y ∈ A. We say that a higher derivation d is inner if there is a sequence a = {an}∞ n=1 in A such that (n + 1)dn+1(x) = Pn k=0 ak+1dn−k(x) − dn−k(x)ak+1, for each n = 0, 1, 2, . . . and x ∈ A. Giving a characterization for inner higher derivations on a torsion free algebra A, we show that each higher derivation on A is inner provided that each derivation on A is inner.

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