The low-temperature properties of some f-electron alloys, in compositi
on close to compounds exhibiting low-temperature instabilities, have b
een found to diverge from the predictions of simple Fermi-lquid models
. We discuss the cases of Y0.8U0.2Pd3 and UCu3.5Pd1.5 for which therma
l and transport properties display significant departures from Fermi-l
iquid behaviour and provide some preliminary microscopic evidence for
anomalous behaviour obtained by measuring NMR relaxation rates T-1(-1)
below 1 K. We have also studied CePd2In in which, below 1.2 K, small
moment antiferromagnetic order coexists with a substantial amount of K
ondo screening. Both the magnetic order and the Kondo screening are st
rongly suppressed by external magnetic fields of the order of 4 T. Fin
ally, we discuss the case of CeAl3 where microscopically a strange inh
omogeneous electronic ground state, characterised by the coexistence o
f two magnetically inequivalent phases, has been identified.