We have measured the specific heat of pure and thoriated (3.3% thorium) UBe13 in the temperature interval 0.3 1.8 K in applied magnetic fields up to 20 T, and find striking qualitative differences between the two systems. For pure UBe13 the electronic coefficient of specific heat el(=Cel(T)/T) is noticeably suppressed by a field of 20 T at 1.8 K; below 1 K, however, this reduction from the low-field, normal-state value tends to zero. For the 3.3% thoriated sample, the high-temperature value of el is relatively insensitive to strong magnetic fields, but at lower temperatures the suppression of el becomes much stronger, reaching nearly 40% at 0.35 K in a field of 20 T. This behavior is similar to that observed in most cerium-based heavy-fermion systems. © 1989 The American Physical Society.