  The short-distance expansion of the heavy-light currents $\bar q\,\gamma^\mu
Q$ and $\bar q\,\gamma^\mu\gamma_5\,Q$ is constructed to order $1/m_Q$, and to
next-to-leading order in renormalization-group improved perturbation theory. It
is shown that the $10\times 10$ anomalous dimension matrix, which describes the
scale dependence of the dimension-four effective current operators in the heavy
quark effective theory, is to a large extent determined by the equations of
motion, heavy quark symmetry, and reparameterization invariance. The
next-to-leading order expressions for the Wilson coefficients at order $1/m_Q$
depend on only five unknown two-loop anomalous dimensions, among them that of
the chromo-magnetic operator.
