Abstract. The concept of tensor analogues of right 2-Engel elements in groups were defined and studied by Biddle and Kappe [1] and Moravec [9]. Using the automorphisms of a given group G, we introduce the notion of tensor analogue of 2-auto Engel elements in G and investigate their properties. Also the concept of 2 ⊗ -auto Engel groups is introduced and we prove that if G is a 2 ⊗ -auto Engel group, then G ⊗ Aut(G) is abelian.Finally, we construct a non-abelian 2-auto-Engel group G so that its non-abelian tensor product by Aut(G) is abelian.

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