  Based on the short-distance expansion of currents in the heavy quark
effective theory, we derive the exact expressions for the heavy-to-heavy meson
and baryon weak decay form factors to order $1/m_Q$ in the heavy quark
expansion, and to all orders in perturbation theory. We emphasize that the
Wilson coefficients in this expansion depend on a kinematic variable $\bar w$
that is different from the velocity transfer $w=v\cdot v'$ of the hadrons. Our
results generalize existing ones obtained in the leading-logarithmic
approximation. Some phenomenological applications are briefly discussed.
