  The present paper is devoted to local and 2-local derivations and
automorphism of complex finite-dimensional simple Leibniz algebras. We prove
that all local derivations and 2-local derivations on a finite-dimensional
complex simple Leibniz algebra are automatically derivations. We show that
nilpotent Leibniz algebras as a rule admit local derivations and 2-local
derivations which are not derivations. Further we consider automorphisms of
simple Leibniz algebras. We prove that every 2-local automorphism on a complex
finite-dimensional simple Leibniz algebra is an automorphism and show that
nilpotent Leibniz algebras admit 2-local automorphisms which are not
automorphisms. A similar problem concerning local automorphism on simple
Leibniz algebras is reduced to the case of simple Lie algebras.
