Local controllability of systems using the topological degree of finite-dimensional set-valued maps is studied. For perturbed linear systems a generalization of the Lee-Markus sufficient condition of local controllability is established. For systems given by a finite family of continuous Vector fields first order controllability condition is obtained. In both cases, a set of control functions sufficient for the local controllability is described, which is homeomorphic with a d-dimensional unit ball, where d is the dimension of the state space.