A new, general approach to constitutive modeling for non-Newtonian liquids (i.e., formulating an equation for the stress tensor in flows with arbitrary kinematics) is proposed and tested, with a particular application to a dilute emulsion of deformable drops. A generalized traceless Oldroyd model is used for the drop-phase contribution to the stress tensor, with five material parameters allowed to be functions of one instantaneous flow invariant. Two choices for this invariant are explored (i) the second invariant I-2 of the rate-of-strain tensor and (ii) the energy dissipation rate. In both versions, all five parameters are found from simultaneously fitting the Oldroyd model to viscometric and extensiometric functions for steady shear and planar extension (PE), respectively, at arbitrary flow intensities. The model predictions are compared to precise (but computationally intensive) results from boundary-integral simulations for several flows different from simple shear or PE. The energy dissipation rate is found to be generally a much better choice for the invariant than I-2, especially for comparable drop and continuous-phase viscosities, and it provides very good accuracy in a wide range of conditions (away from drop breakup). Test examples include mixed planar flow, uniaxial/biaxial extension, flow in a cavity with a moving wall, and flow past a macroscopic sphere. Unlike small-deformation theories, the present approach can be extended to large-strain flows of highly concentrated emulsions. (C) 2014 The Society of Rheology.