Abstract: Aimed at analyzing the singularity of double gimbal control moment gyroscopes(DGCMGs), a gimbal reference frame, an ε-δ definition of apparent and concealed singular points, three sorts of singular points, system momentum taylor series expanded formula at singular point and a determination of null motions were proposed. The relation between singularity of the system and parallelism of each gyroscope angular momentum was discussed. It was strictly proved that the DGCMGs with constant velocity and equal angular momentum and without limit of configuration, has the property that inside singular points must be concealed singular ones. The views above were examined through the numerical simulation of minimal apparent singular points of three orthogonal configuration’s 20° latitude circle.