  We calculate light-cone distribution amplitudes for non-relativistic bound
states, including radiative corrections from relativistic gluon exchange to
first order in the strong coupling constant. We distinguish between bound
states of quarks with equal (or similar) mass, m_1 ~ m_2, and between bound
states where the quark masses are hierarchical, m_1 >> m_2. For both cases we
calculate the distribution amplitudes at the non-relativistic scale and discuss
the renormalization-group evolution for the leading-twist and 2-particle
distributions. Our results apply to hard exclusive reactions with
non-relativistic bound states in the QCD factorization approach like, for
instance, (B_c -> eta_c l nu) or (e^+ e^- -> J/psi eta_c). They also serve as a
toy model for light-cone distribution amplitudes of light mesons or heavy B and
D mesons, for which certain model-independent properties can be derived. In
particular, we calculate the anomalous dimension for the B meson distribution
amplitude phi_B^-(w) in the Wandzura-Wilczek approximation and derive the
according solution of the evolution equation at leading logarithmic accuracy.
