Existence of nonlinear velocity constraints outside the Newtonian model

A mechanical system is described by constraints that may be nonlinear in the velocity. Existence conjecture. The existence of mechanical systems with nonlinear constraints in the velocity must be sought outside of the Newtonian model. The paper presents nonlinear-constraint equations as an extension of the classical Chaplygin equations and argues that such systems are not supplied by the Newtonian model; no resolution of this conjecture is given.