2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/40340Five different versions of the three-dimensional (3D) reduction of the Bethe-Salpeter (BS) equation in the instantaneous approximation for kernel of BS equation for the two-fermion systems are formulated. The normalization condition for the bound-state wave function in all versions are derived. Further, the 3D reduction of BS equation without instantaneous approximation for the kernel of BS equation is formulated in the quasi-potential approach. Except of the Salpeter version, other four versions have the correct one-body limit (Dirac equation) when mass of one of constituent fermions tends to infinity. Application of these versions for investigation of the different properties of the q bar q bound systems are considered.45 pages, 2 postscript figures, uses RevTeX styleHigh Energy Physics - Phenomenologytext