Abstract: In this paper, we prove that for holonomic nonconservative dynamical systems the integral invariant of Poincare and Cartan and the universal integral invariant of Poincare do not exist. Instead of that, we introduce the integral variants of Poincare and Car-tan's type and of Poincare type for holonomic nonconservative dynamical systems, and use those variants to solve the problem of nonlinear vibration. We also prove that the integral invariants introduced in references 1 and 2 are merely the basic inte...