We discuss strong deviations from the signatures of a heavy Landau-Fermi li
quid already at p = 0 that are observed for normal (n)-state CeCu2Si2, for
CeNi2Ge2 and YbRh2Si2. No quantum critical point could yet be established i
n the case of CeNi2Ge2. For this compound, preliminary investigations of th
e chemical phase diagram have revealed certain similarities to CeCu2Si2. Th
e non-Fermi-liquid (NFL) effects observed for YbRh2Si2 suggest a quasi-2D s
ystem of magnetic fluctuations. We also discuss briefly disparities between
resistivity and specific-heat results in all three compounds as well as th
e relationship between a NFL n-state and the occurrence of heavy-fermion su
perconductivity. (C) 2000 Elsevier Science B.V. All rights reserved.