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Effects of relative motion between moving fuel and neutrons are usually not considered in the analysis of Circulating Fuel Reactors (CFRs). In this study, we formulate neutron transport equation for CFRs in a hydrodynamic representation in terms of velocities relative to moving fuel. Using the P1 approximation in the comoving transport equation, the diffusion equation for CFRs is obtained. Mass transport of precursors is considered in the formulations. Comoving frame CFRs equations are analytically solved for critical slab problem and a closed form criticality condition is obtained. Comoving representation has introduced corrections to Eulerian cross sections arising from the acceleration term. Hydrodynamics coupling has posed density modifications to cross sections. A parametric study of corrective terms is carried out to calculate effects of these corrections on a generic MSR and on Molten Salt Breeder Reactor (MSBR).