Let G be a group. The Lie algebra sl2 of 2 × 2 traceless matrices over a field K can be endowed up to isomorphism, with three distinct non-trivial G-gradings induced by the groups Z2, Z2×Z2 and Z. It has been recently shown (Koshlukov, 2008 [8]) that for each grading the ideal of G-graded identities has a finite basis.In this paper we prove that when char(K)=0, the algebra sl2 endowed with each of the above three gradings has an ideal of graded identities IdG(sl2) satisfying the Specht property, i.e., every ideal of graded identities containing IdG(sl2) is finitely based. © 2013 Elsevier Inc.389 622Bahturin, Y., Kochetov, M., Classification of group gradings on simple Lie algebras of types A, B, C and D (2010) J. Algebra, 324 (11), pp. 2971-2989Drensky, V., (1999) Free Algebras and PI-Algebras, , Springer-Verlag, SingaporeDrensky, V., Identities in Lie algebras (1974) Algebra Logika. Algebra Logic, 13, pp. 150-165. , (in Russian)English translation in:Giambruno, A., Zaicev, M., Polynomial identities and asymptotic methods (2005) Math. Surveys Monogr., 122Higman, G., Ordering by divisibility in abstract algebras (1952) Proc. Lond. Math. Soc. (3), 2, pp. 326-336James, G., Kerber, A., The Representation Theory of the Symmetric Group (1981) Encyclopedia Math. Appl., 16. , Addison-Wesley, LondonKemer, A.R., Ideals of Identities of Associative Algebras (1991) Transl. Math. Monogr., 87. , American Mathematical Society, Providence, RIKoshlukov, P., Graded polynomial identities for the Lie algebra sl2(K) (2008) Internat. J. Algebra Comput., 18 (5), pp. 825-836Razmyslov, Y., Finite basing of the identities of a matrix algebra of second order over a field of characteristic zero (1973) Algebra Logika. Algebra Logic, 12 (1), pp. 47-63. , (in Russian)English translation in:Razmyslov, Y., Identities of Algebras and Their Representations (1994) Transl. Math. Monogr., 138. , American Mathematical Society, Providence, RIRepin, D.V., Graded identities of a simple three-dimensional Lie algebra (2004) Vestn. Samar. Gos. Univ. Estestvennonauchn. Ser., 2 (SPEC. ISSUE.), pp. 5-16. , (in Russian)Vaughan-Lee, M.R., Varieties of Lie algebras (1970) Quart. J. Math. Oxford Ser. (2), 21, pp. 297-308