The half-Heusler compounds YPdBi and TbPdBi, while having a similar band structure, exhibit different magnetic properties. YPdBi is a diamagnet, while TbPdBi shows antiferromagnetic order below 5.5 K. Both are superconductors with Tc\1 K for YPdBi and Tc\1.75 K for TbPdBi. Such a contrast in properties between these two compounds opens a question about the effects of band structure or magnetic correlations on superconductivity. Using the combination of a tunnel diode oscillator and a commercial dilution refrigerator, we measured the temperature-dependent magnetic penetration depth \Δ\T) in single crystals of YPdBi and TbPdBi, down to temperatures as low as 0.1 K. We found that the penetration depths of both compounds do not show an exponential temperature dependence and saturation at low temperatures, as expected for conventional BCS superconductors. Instead, in both compounds, the penetration depth can be described by a power law \Δ\T)=A\Tn. The coefficient A was found to be about 50% smaller in TbPdBi, but the exponents are very similar, n=2.76\0.04 in YPdBi and n=2.6\0.3 in TbPdBi, respectively. Our results suggest unconventional superconductivity in both YPdBi and TbPdBi. \ 2018 American Physical Society.