  We calculate the dynamical spin response of Kondo impurity and Kondo lattice
systems within a semiphenomenological Fermi liquid description, at low
temperatures $T<T_K$, the Kondo temperature, and low magnetic fields $B \ll k_B
T_K/g\mu_B$. Fermi liquid parameters are determined by comparison (i) with
microscopic theory (numerical renormalization group) for the impurity model and
(ii) with experiment for the lattice model. We find in the impurity case that
the true impurity spin resonance has a width of the order of $T_K$ and
disappears altogether if the $g$-factors of impurity spin and conduction
electron spin are equal. However, there is an impurity-induced resonance
contribution at the conduction electron resonance. The latter is broadened by
spin lattice relaxation and is usually unobservable. In contrast, for the
Anderson lattice in the Kondo regime we find a \textit{sharp} ESR resonance
line only slightly shifted from the local resonance and broadened by spin
lattice relaxation, the latter significantly reduced by both the effects of
heavy fermion physics and ferromagnetic fluctuations. We conjecture that our
findings explain the sharp ESR-lines recently observed in several heavy fermion
compounds.
