Abstarct: We introduce and investigate two new subclasses of the function class ∑ of bi- univalent functions defined in the open unit disk, which associated with the Hohlov operator , that is, a familiar special case of the widely- (and extensively-) investigated Dziok- Srivastava linear operator. 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 the results are also pointed out.