Certain chemically substituted Ce and U compounds have low-temperature physical properties that exhibit non-Fermi-liquid (NFL) characteristics and apparently constitute a new class of strongly correlated f-electron materials. The NFL behaviour takes the form of weak power law or logarithmic divergences in the temperature dependence of the physical properties that scale with a characteristic temperature T-0, which, in some systems, can be identified with the Kondo temperature T-K. These systems have complex temperature T-chemical substituent composition x phase diagrams, which contain regions displaying the Kondo effect, NFL behaviour, spin glass freezing, magnetic order, quadrupolar order, and, sometimes, even superconductivity. Possible origins of the NFL behaviour include a multichannel Kondo effect and fluctuations of an order parameter in the vicinity of a second-order phase transition at T = 0 K. Recent experiments on the systems Y1-xUxPd3 and U(1-x)M(x)Pd(2)Al(3) (M = Th, Y) are reviewed. In the Y1-xUxPd3 and U1-xThxPd2Al3 systems, the low-temperature physical properties in the NFL regime scale with the U concentration and T-K, suggesting that single-ion effects are responsible for the NFL behaviour.