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Based on an extension of the Foldy--Wouthuysen method to two-body equations,the problem of expansion of equal-time relativistic equations for two Diracparticles in powers of $1/c$ to higher orders is considered. For the case oftwo particles with unequal masses, the transformed Hamiltonian in a generaleven-even form is obtained to order $1/c^4$. It is found that certain extraterms, which can be eliminated by an additional unitary transformation, arisein the expansion in higher orders, depending on the order of application of thegenerating functions in the first iteration. As examples for illustration, theBreit equation and the Salpeter equation with the Breit interaction are takenand their reduction to approximate forms including all the $1/c^{4}$-orderterms is carried out using the method under consideration. The obtained resultsmay be applied for the nonrelativistic expansion of two-body wave equationswith various interaction potentials to higher orders, for the investigation oftheir features and symmetries, and may also be useful in the study of lightatoms.

On expansion of equal-time relativistic two-body wave equations in powers of 1/c to higher orders