  In this paper we have obtained some dynamics equations, in the presence of
nonlinear nonholonomic constraints and according to a lagrangian and some
Chetaev-like conditions. Using some natural regular conditions, a simple form
of these equations is given. In the particular cases of linear and affine
constraints, one recovers the classical equations in the forms known
previously, for example, by Bloch and all \cite {Bl, BKMM}. The case of
time-dependent constraints is also considered. Examples of linear constraints,
time independent and time depenndent nonlinear constraints are considered, as
well as their dynamics given by suitable lagrangians. All examples are based on
classical ones, such as those given by Appell's machine.
