  The quantum electrodynamic theory of the nuclear recoil effect in atoms to
all orders in \alpha Z and to first order in m/M is considered. The complete
\alpha Z - dependence formulas for the relativistic recoil corrections to the
atomic energy levels are derived in a simple way. The results of numerical
calculations of the recoil effect to all orders in \alpha Z are presented for
hydrogenlike and lithiumlike atoms. These results are compared with analytical
results obtained to lowest orders in \alpha Z. It is shown that even for
hydrogen the numerical calculations to all orders in \alpha Z provide most
precise theoretical predictions for the relativistic recoil correction of first
order in m/M.
