  We present a systematic study of higher-twist distribution amplitudes (DAs)
of the B-meson which give rise to power-suppressed $1/m_B$ contributions to
B-decays in final states with energetic light particles in the framework of QCD
factorization. As the main result, we find that the renormalization group
equations for the three-particle distributions are completely integrable in the
large $N_c$ limit and can be solved exactly. General properties of the
solutions are studied. We propose simple models for higher-twist DAs which
satify all existing constraints and can be used in phenomenological studies.
