Non-Fermi-liquid (NFL) behavior in three-dimensional metals with stron
g electron correlations can have different origins, viz. collective or
single-ion effects. The former is manifest at a magnetic instability
where the system changes from a nonmagnetic to a magnetic ground state
as a function of some parameter like concentration or pressure. We re
view the properties of the exemplary NFL heavy-fermion system CeCu6-xA
ux at this magnetic instability, i.e. a logarithmic divergence of the
specific-heat coefficient gamma(T)= C/T, a cusp in the magnetic DC sus
ceptibility chi(T) for T --> 0, and a T-linear contribution Delta rho
to the electrical resistivity, as opposed to the Fermi-liquid behavior
gamma similar to chi approximate to const, Delta rho similar to T-2 f
ound in many heavy-fermion systems, including the parent compound CeCu
6. Single-ion effects leading to NFL behavior are overscreening of mag
netic or quadrupolar degrees of freedom of a magnetic impurity or a di
stribution of Kondo temperatures in a disordered alloy. Similarities a
nd differences of the NFL phenomenology between these scenarios will b
e reviewed.