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We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose the dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have 1-dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning 2-local derivations of such algebras are investigated and an example of solvable Leibniz algebra given such that any 2local derivation on it is a derivation, but which admit local derivations which are not derivations.

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The present paper is devoted to study 2-local derivations on infinitedimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations on the Witt algebra as well as on the positive Witt algebra are (global) derivations, and give an example of infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.