  The main goal of this paper is to give some construction results of
BiHom-post-Lie algebras which are a generalization of both post-Lie-algebras
and Hom-post-Lie algebras. They are the algebraic structures behind the
$\mathcal{O}$-operator of BiHom-Lie algebras. They can be also regarded as the
splitting into three parts of the structure of a BiHom-Lie-algebra. Moreover we
develop the representation theory of BiHom-post-Lie algebras on a vector space
$V$. We show that there is naturally an induced representation of its
sub-adjacent Lie algebra.
