For nonholonomic systems with nonlinear constraints the conditions of the validity of the Hamiltonian principle in Golder, Voronets and Suslov forms are investigated. It is shown that all these forms may be transformed one to another. The necessary and sufficient conditions are obtained for which the Hamiltonian principle has the character of rhe conditional variational principle. These conditions are analogous to them which have been earlier established for the applicability of the generalized Hamilton-Jacobi method.