  We calculate the leading mass-suppressed two-loop contribution, proportional
to alpha_s^3/(m_q r^2), to the potential of a heavy quark-antiquark system.
This contribution originates in the nonabelian nature of quantum chromodynamics
(QCD) and has no analogue in quantum electrodynamics (QED). For this purpose,
we elaborate a technique based on the implementation of the threshold expansion
within the effective theory of nonrelativistic QCD (NRQCD). We discuss
phenomenological implications of our result for heavy-quarkonium physics. We
also confirm a previous result for the two-loop O(alpha_s^2) correction to the
static potential.
