  We calculate the relativistic corrections of relative order (Z alpha)^2$ to
the two-photon decay rate of higher excited S and D states in ionic atomic
systems, and we also evaluate the leading radiative corrections of relative
order alpha (Z alpha)^2 ln[(Z alpha)^(-2)]. We thus complete the theory of the
two-photon decay rates up to relative order alpha^3 ln(alpha). An approach
inspired by nonrelativistic quantum electrodynamics is used. We find that the
corrections of relative order (Z alpha)^2 to the two-photon decay are given by
the zitterbewegung, the spin-orbit coupling and by relativistic corrections to
the electron mass, and by quadrupole interactions. We show that all corrections
are separately gauge-invariant with respect to a "hybrid" transformation from
velocity to length gauge, where the gauge transformation of the wave function
is neglected. The corrections are evaluated for the two-photon decay from 2S,
3S, 3D, and 4S states in one-electron (hydrogenlike) systems, with 1S and 2S
final states.
