Let (p, q) ∈ (0, 1). Let the function f be analytic in |z| < 1. Further, let the (p, q) be differential operator defined as ∂p,qf(z)=f(pz)−f(qz)z(p−q),|z|<1. In the current investigation, the authors apply the (p, q)-differential operator for few subclasses of univalent functions defined by quasi-subordination. Initial coefficient bounds for the defined new classes are obtained. © 2018, Springer Nature Switzerland AG.