  In this paper we introduce and investigate two new subclasses of the function
class $\Sigma$ of bi-univalent functions of complex order defined in the open
unit disk, which are associated with the Hohlov operator, and satisfying
subordinate conditions. Furthermore, we find estimates on the Taylor-MacLaurin
coefficients $|a_2|$ and $|a_3|$ for functions in these new subclasses. Several
known or new consequences of these results are also pointed out.
