  We consider the Lagrange density of non-relativistic Quantum Chromodynamics
expanded up to order $1/m^2$, where $m$ is the heavy quark mass, and compute
several matching coefficients up to two-loop order. Our results are building
blocks for next-to-next-to-next-to-leading logarithmic and
next-to-next-to-next-to-next-to-leading order corrections to the threshold
production of top quark pairs and the decay of heavy quarkonia. We describe the
techniques used for the calculation and provide analytic results for a general
covariant gauge.
