Abstract: This paper proves that the canonical equations of Poincarè-Chtaev are more general Hamilton equations in terms of noncanonical variables. This shows that the generalized Lagrange equations and the generalized Hamilton equations in terms of remainder coordinates, as well as the Euler-Lagrange equations in terms of quasi-coordinates are particular cases of the Poincarè-Chtaev equations. And then, the theory is extended to the above systems. The application of Poincarè-Chetaev equations in dynamics of nonholo...