  The Drell-Hearn-Gerasimov sum rule for the deuteron is studied in nuclear
effective field theory. The low-energy theorem for the spin-dependent Compton
amplitude $f_1(\omega)$ is derived to the next-to-leading order in low-energy
expansion. The spin-dependent photodisintegration cross section
$\sigma^P-\sigma^A$ is calculated to the same order, and its contribution to
the dispersive integral is evaluated.
