We have explored the vicinity of the antiferromagnetic quantum critica
l point in the related heavy fermion metals CePd2Si2 and CeNi2Ge2 as a
function of hydrostatic pressure. The normal state resistivity of the
antiferromagnet CePd2Si2 near the critical pressure, at which magneti
c order disappears, varies as rho similar to T-x(1.1 < x < 1.4) over n
early two orders of magnitude in temperature up to about 30 K. This an
omalous form for the resistivity appears to defy not only Fermi-liquid
theory, but also simple phenomenological models for the effect of spi
n fluctuations close to a quantum critical point. An analogous unconve
ntional behaviour is observed in the ambient pressure resistivity of t
he electronically and structurally equivalent, non-magnetic metal CeNi
2Ge2. At pressures above 15 kbar, a new and unexpected superconducting
transition appears in CeNi2Ge2 below 220 mK, which rises to higher te
mperatures with increasing pressure, reaching 400 mK at 26 kbar.