In the present chapter it is shown that all known types of equations of motion of nonholonomic systems are equivalent since they can be obtained from the invariant vector form of the law of motion of mechanical system with ideal constraints. The nonholonomicity of constraints, which does not allow for the equations of motion to be represented in the form of Lagrange's equations of the second kind, turns out to be most clearly if the equations of motion of nonholonomic system are written in quasicoordinates. In the case of linear constraints these equations are generated here by three different methods. This permits us to consider the problem of nonholonomicity from three different points of view.