The double-ring gear reducer (DRGR) is a novel planetary gearing with small tooth-number difference. It has apparent advantages over common gear reducers such as large transmission ratio, high loading capacity, compact volume, low fabricating cost and wide adaptability. To obtain actual loading state of the components, a DRGR featuring a phase-angle difference of non-180 degrees and complete equilibrium has been investigated in details. Key influences were taken into account including the elasticity of high-speed shafts, gear-couplers, meshing teeth and bearings as well as additional rotation angle of the supporting shaft. The compatibility conditions of elastic deformations were derived by means of the so-called force-displacement hybrid method. Finally, the elasto-quasi-static equation of the over-constrained mechanism was developed.