<p>In this paper, we study the nonlinear orbital stability of soliton solutions of the Schamelequation with modular nonlinearity describing solitary waves of different polarities. Theproof of the nonlinear stability of these solutions is established within the framework of the general theory forthe stability of bound states that decrease rather rapidly on the real axis and correspondto soliton solutions ofthe translationally invariant infinite-dimensional Hamiltonian system (which is the Schamel equation under consideration).The required stability is established based on verification of the formulated stability conditions.These conditions, being sufficient, imply checkingthe spectral properties of the operator resulting fromlinearization of a functional that makes sense of the Lyapunov function. Generally speaking, for translationally invariant differential equations it is impossible to consider the usual stability, when a small perturbation of the solution remains small. The solutions of such equations are subject to investigation by the presence of orbital stability, i. e., stability “up to shear accuracy”. As a result,it is not possible to construct a Lyapunov function (functional) in the problems of stability of boundary states, which would have a local minimumdetermined by a neighborhood system of the basic functionalspace of the problem.If the conditions of orbital stability are met, the Lyapunov function has a conditionallocal minimum, i. e., a local minimum on some nonlinearsubmanifold of the basic functional space of the systemof equations at a point defined by the solution to beinvestigated for stability. This nonlinear submanifold, asa rule, is determined by the condition of the constancy of the functional,the invariance of which, by virtue of the basic system of equations, is associatedwith the translational invariance of the problem.</p>