The two‐fermion relativistic wave equations of constraint theory are reduced, after expressing the components of the 4×4 matrix wave function in terms of one of the 2×2 components, to a single equation of the Pauli–Schrödinger type, valid for all sectors of quantum numbers. The potentials that are present belong to the general classes of scalar, pseudoscalar, and vector interactions and are calculable in perturbation theory from Feynman diagrams. In the limit when one of the masses becomes infinite, the equation reduces to the two‐component form of the one‐particle Dirac equation with external static potentials. The Hamiltonian, to order 1/c2, reproduces most of the known theoretical results obtained by other methods. The gauge invariance of the wave equation is checked, to that order, in the case of QED. The role of the c.m. energy dependence of the relativistic interquark confining potential is emphasized and the structure of the Hamiltonian, to order 1/c2, corresponding to confining scalar potentials, is displayed. © 1994 American Institute of Physics.