In this paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions of complex order dened in the open unit disk, which are associated with q-hypergeometric functions, satisfying subordinate conditions. Furthermore, we nd estimates on the coefficients |a2| and |a3| for functions in these new subclasses. Several consequences of the results are also mentioned. © Balkan Society of Geometers, Geometry Balkan Press 2015.