The non-Fermi-liquid (NFL) behavior observed in the low temperature specific heat $C(T)$ and magnetic susceptibility $chi(T)$ of f-electron systems is analyzed within the context of a recently developed theory based on Griffiths singularities. Measurements of $C(T)$ and $chi(T)$ in the systems $Th_{1-x}U_{x}Pd_{2}Al_{3}$, $Y_{1-x}U_{x}Pd_3$, and $UCu_{5-x}M_{x}$ (M = Pd, Pt) are found to be consistent with $C(T)/T propto chi(T) propto T^{-1+lambda}$ predicted by this model with $lambda <1$ in the NFL regime. These results suggest that the NFL properties observed in a wide variety of f-electron systems can be described within the context of a common physical picture.