Measurements of the temperature-dependent specific heat and thermal expansion coefficient near a T=0 magnetic-nonmagnetic boundary, accessed in CeRh2Si2 by application of pressure and in CeRh2-xRuxSi2 at ambient pressure by chemical substitution, emphasize the role of disorder in producing non-Fermi-liquid behavior. Interestingly, superconductivity also develops near this boundary in some crystallographically-ordered Ce-based heavy-fermion compounds. [CeRh2-xRuxSi2, specific heat, thermal expansion, susceptibility, non-Fermi-liquid]. © 1998, The Japan Society of High Pressure Science and Technology. All rights reserved.