The purpose is to introduce the notions of 3-Bihom--Lie algebras and 3-pre- Bihom--Lie algebras. The authors describe their constructions and express the related lemmas and theorems. Also, they define the 3-Bihom--Leibniz algebras and show that a 3-Bihom--Lie algebra is a 3-Bihom--Leibniz algebra with the -Bihom-skew symmetry property. Moreover, a combination of a 3-Bihom--Lie algebra bracket and a Rota-Baxer operator gives a 3-pre-Bihom--Lie algebra structure.
