  It is demonstrated how perturbative O(alpha_s^2) relativistic corrections to
the non-relativistic stable heavy quark-antiquark production cross section in
e^+e^- annihilation based on a Coulombic QCD potential can be systematically
calculated using the concept of effective field theories. The O(alpha_s^2)
corrections from the relativistic energy-momentum relation, the relativistic
phase space corrections and the O(alpha_s^2) corrections involving the group
theoretical factors C_F^2 and C_F T are determined explicitly. For the case of
$t\bar t$ production the sum of these corrections amounts to 3% - 7% over the
whole threshold regime and is insensitive to variations in the top width.
Perturbative O(alpha_s^2) corrections to the leptonic decay width of heavy
quark-antiquark $^3S_1$ vector resonances are extracted.
