Semiclassical Quantization Condition for a Relativistic Bound System of Two Equal-Mass Fermions

New relativistic semiclassical quantization conditions are obtained for a system of two equal-mass fermions interacting via nonsingular confining quasipotentials and quasipotentials of the funnel type. The quantization conditions are specified in the pseudoscalar, pseudovector, and vector cases. The respective analysis is performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of a bound system formed by two relativistic spin particles of equal mass.