  The analytical calculation of the complete $\alpha\,(Z\,\alpha)^6$ one-loop
radiative correction to energies of two-body systems with the angular momenta
$l>0$, consisting of a pointlike particle and an extended-size nucleus with
arbitrary masses and spin 1/2, is presented. The obtained results apply to a
wide variety of two-body systems, such as hydrogen, muonium, positronium, and
antiprotonic atoms.
