The low-temperature specific heat at magnetic fields of 0 and 7 T, dc susceptibility, and resistivity data for two samples of TiBe2.00 and one sample of TiBe1.94O0.05 are presented. The temperature dependence of the low-temperature specific heats of all three samples of TiBe2 is found to include an important T3lnT term, confirming that spin fluctuations are present in TiBe2, the first metal besides UAl2 where such a T3lnT term has been found. Evidence for a magnetic impurity present in one of the two pure TiBe2 samples is inferred from the measurements and confirmed by the same measurements on the sample with oxygen intentionally added. The impurity is thought to increase the low-temperature susceptibility, shape the resistivity, and cause a 3% decrease of the low-temperature specific heat in a 7-T field at lower temperatures. At higher temperatures in the impure samples, and at all temperatures in the purer sample of TiBe2, there is no change from the zero-field values in the specific heat to ± 1% in a 7-T field, in contradiction to the theoretical prediction of Béal-Monod. These field results are discussed with respect to the recent measurements of the low-temperature specific heats in a field of Pd and LuCo2. Previous low-temperature specific-heat results on TiBe2.06 and TiBe1.79Cu0.21 are also discussed. © 1982 The American Physical Society.