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In the present paper we prove that every 2-local inner derivation on the Liering of skew-adjoint matrices over a commutative $*$-ring is an innerderivation. We also apply our technique to various Lie algebras ofinfinite-dimensional skew-adjoint matrix-valued maps on a set and prove thatevery 2-local spatial derivation on such algebras is a spatial derivation. Wealso show that every local spatial derivation on the above Lie algebras is aderivation.

Local and 2-local derivations on Lie matrix rings over commutative involutive rings