Collective center-of-mass variables are introduced in the Lagrangian formalism of the relativistic classical mechanics of directly interacting particles. It is shown that the transition to the Hamiltonian formalism leads to the Bakamjian-Thomas model. The quantum-mechanical system consisting of two spinless particles is investigated. Quasi-relativistic corrections to the discrete energy spectrum are calculated for some Coulomb-like interactions having field theoretical analogues.

12 pages, Latex2e