Conceptions of strong stability and strong instability of a linear periodic Hamiltonian system of differential equations for a given Hamiltonian perturbation are introduced. The systems subjected to action of periodic perturbations-arbitrary Hamiltonian and the given Hamiltonian ones. A theorem about sufficient conditions of its strong stability and instability is proved. In the frames of linear periodic Lagrange equations of the second kind, the influence of hygroscopic forces as well as given perturbing dissipative and non-conservative forces on their strong stability and instability is studied in satisfaction of critical relationships of the combination resonances.