  We present inelastic neutron scattering measurements on the intermetallic
compounds Ce(Ru$_{1-x}$Fe$_x$)$_2$Ge$_2$ ($x$=0.65, 0.76 and 0.87). These
compounds represent samples in a magnetically ordered phase, at a quantum
critical point and in the heavy-fermion phase, respectively. We show that at
high temperatures the three compositions have the identical response of a local
moment system. However, at low temperatures the spin fluctuations in the
critical composition are given by non-Fermi-liquid dynamics, while the spin
fluctuations in the heavy fermion system show a simple exponential decay in
time. In both compositions, the lifetime of the fluctuations is determined
solely by the distance to the quantum critical point. We discuss the
implications of these observations regarding the possible origins of
non-Fermi-liquid behavior in this system.
