Nonlinear controllability theory is utilized to investigate the small-time local controllability (STLC) of the combined dynamics of a spacecraft with control moment gyros (CMGs). Specifically speaking, with three or more independent-type CMGs, the dynamics are STLC from, and hence can be stabilized via time-invariant piecewise continuous feedback laws to, the equilibrium as long as the CMGs never reach certain definite singularities and semidefinite singularities at the equilibrium. These results are then applied to a spacecraft carrying four pyramid-type CMGs and further extended to a spacecraft using roof-type CMGs, in addition to the special case of two CMGs. (C) 2014 Elsevier Ltd. All rights reserved.