Using heavy quark effective field theory, exponentiation of Sudakov do
uble logarithms, and perturbative factorization theorems for exclusive
processes, we calculate the amplitude for the semileptonic decay of m
esons with a single, very heavy quark into pi and rho for a large hadr
onic recoil momentum. A formula for these large-recoil widths is obtai
ned in terms of two-particle wave functions of the heavy and light mes
ons and applied to semileptonic decays of the B.