This paper puts forward sufficient conditions for local controllability of abnormal systems, that is, in the case when a linearization of a system at the admissible process under consideration is not controllable. Sufficient conditions for local controllability of a nonlinear system at an equilibrium point are obtained as an application of these results. The proof of the sufficient conditions for local controllability is based on the implicit function theorem, which is meaningful near a singular point of the mapping defining the equation. This theorem is proved in the second section.