  We have completed the calculation of pure-recoil corrections of order $(Z
\alpha)^6$ to Coulombic bound states of two spin-1/2 fermions without
approximation in the particle masses. Our result applies to systems of
arbitrary mass ratio such as muonium and positronium, and also hydrogen and
muonic hydrogen (with the neglect of proton structure effects). We have shown
how the two-loop master integrals that occur in the relativistic region can be
computed in analytic form, and suggest that the same method can be applied to
the three-loop integrals that would be present in a calculation of order $(Z
\alpha)^7$ corrections.
