Abstract. In 1994, Moneyhun introduced and studied the concept of isoclinism in Lie algebras. Moghaddam and parvaneh in 2009 introduced and gave some properties of isoclinism of a pair of Lie algebras. In this paper we introduce the concept of relative n-isoclinism between two pairs of Lie algebras. They form equivalence classes and we show that each equivalent class contains an n-stem pair of Lie algebras. We also show that for a relative n-isoclinism family of Lie algebras C say, consists of (M;L) such that L is finitely generated and [M;n L] is finite dimension, then there exists an n-stem pair of Lie algebras (R; S) ∈ C such that dim([R;n-1 S] = min{dim([M;n-1 L]); for all (M;L) ∈ C}:

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