The increasing valency of the Yb ion when Cu is substituted by Al in YbCu5-xAlx causes a magnetic instability at a critical concentration x(cr) approximate to 1.5. Alloys in the vicinity of x(cr) are characterised by a - ln T contribution to the specific heat and substantial deviations of the electrical resistivity from a T-2 dependence. Similar features have been observed in a number of Ce and U based systems, and are considered as typical fingerprints of a non-Fermi-liquid behaviour. (C) 1999 Elsevier Science B.V. All rights reserved.