  We perform a calculation of quantum electrodynamics effects in excited states
with $l>1$ of arbitrary two-body systems up to $\alpha^6\,\mu$ order. The
obtained results are valid for hadronic atoms, as long as the strong
interaction effects are negligible. We demonstrate that for circular states
with $l\sim n$, the effective expansion parameter is $Z\,\alpha/n$, which
extends the applicability of the derived formulas to heavy ions. Moreover,
inclusion of higher-order terms is feasible, which indicates that accurate
measurements of excited states of, for example, muonic or antiprotonic
hydrogenic ions can be used to determine the fundamental constants and to
search for the existence of yet unknown long-range interactions.
