A Conditional Moment Closure (CMC) formulation of the species transport equation including differential diffusion is presented. Further, the CMC equation for conditional enthalpy is also derived. The objectives of the present study are to (1) derive the CMC equations including the differential effects for both the species and enthalpy in the context of hydrogen combustion, (2) implement the new CMC equations in RANS in two dimensions without any cross-stream averaging and (3) evaluate the benefits and drawbacks of the present CMC calculations applied to a non-premixed hydrogen-air flame. The current study is focused on improving the NO concentration near the nozzle. Predictions of the flow and mixing fields and CMC results for the temperature, major chemical species, and NO concentrations are compared with the experimental data. A budget of the terms in the CMC equations for the differentially diffusing chemical species is investigated. The model is shown to have a prominent effect on NO predictions, with an improvement in the regions close to the nozzle. Some possible sources of modeling discrepancy are identified. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.