Let G be a group with a finite set of generators x1, x2,…,xn and a recursive set of defining relators in the generators. Then an endomorphism η of G is completely determined by the images of the generators , and hence by the n-tuple of words in x, (w1,…,wn). This allows the formulation of algorithmic problems about endomorphisms and automorphisms. For example, can one decide if a given n-tuple of words represents an endomorphism, and if so, an automorphism? Some results on these questions may be found in  and . Here we shall be concerned with a similar problem: given that an n-tuple of words represents an automorphism of the group G, does there exist an algorithm which decides if the automorphism is inner?