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