We report relative measurements of the n− d longitudinal spin-dependent total cross-section difference ( σ L ) d , at E n (lab) = 5.0, 6.88, and 9.0 MeV. The deuteron target was polarized via dynamic nuclear polarization at 250 mK in a 2.5-T external magnetic field. The target polarization was monitored by nuclear magnetic resonance and was calibrated by a ( σ L ) d measurement at E n (lab) = 1.18 MeV. The polarized neutron beams were produced through the 3 H( p, n) 3 He and 2 H( d, n) 3 He reactions. The neutron polarizations were determined either by direct measurement or from known or calculated polarization-transfer coefficients. The results for ( σ L ) d show agreement with theoretical calculations based on nucleon-nucleon potential models but are not of sufficient precision to distinguish the presence or absence of three-nucleon force contributions to the cross sections.