  The aim of this paper is to introduce $n$-ary BiHom-algebras, generalizing
BiHom-algebras. We introduce an alternative concept of BiHom-Lie algebra called
BiHom-Lie-Leibniz algebra and study various type of $n$-ary BiHom-Lie algebras
and BiHom-associative algebras. We show that $n$-ary BiHom-Lie-Leibniz algebra
can be represented by BiHom-Lie-Leibniz algebra through fundamental objets.
Moreover, we provide some key constructions and study $n$-ary BiHom-Lie
algebras induced by $(n-1)$-ary BiHom-Lie algebras.
