The neutron total cross sections of 249Bk and 249Cf have been measured from 0.03 to 100 eV using the Oak Ridge Electron Linear Accelerator as a source of pulsed neutrons. The 1.6-mm-diam cylindrical transmission samples initially contained up to 5.3 mg of 98% 249Bk and 2% 249Cf; 4.5 yr later, when the final measurements were made, the composition of the samples had become 2.5% 249Bk, 96.9% 249Cf and 0.6% 245Cm. Samples were cooled with liquid nitrogen to reduce Doppler broadening. Thirty-nine resonances were identified in 249Bk and analyzed using a single-level Breit-Wigner formalism. Fifty-five resonances were identified in 249Cf and analyzed using an R-matrix multilevel formalism. The resonance parameters obtained have been used to determine the average level spacings and the s-wave neutron and fission strength functions. Where possible, bound-level parameters were derived to fit the thermal neutron total cross-section data.