  The dynamical spin susceptibility is studied in the magnetically-disordered
phase of heavy-Fermion systems near the antiferromagnetic quantum phase
transition. In the framework of the $S=1/2$ Kondo lattice model, we introduce a
perturbative expansion treating the spin and Kondo-like degrees of freedom on
an equal footing. The general expression of the dynamical spin susceptibility
that we derive presents a two-component behaviour: a quasielastic peak as in a
Fermi liquid theory, and a strongly q-dependent inelastic peak typical of a
non-Fermi liquid behaviour. Very strikingly, the position of the inelastic peak
is found to be pushed to zero at the antiferromagnetic transition with a
vanishing relaxation rate. The comparison has been quantitatively made with
Inelastic Neutron Scattering (INS) experiments performed in $CeCu_{6}$ and
$Ce_{1-x}La_{x}Ru_{2}Si_{2}$. The excellent agreement that we have found gives
strong support to a two-band model with new prospects for the study of the
quantum critical phenomena in the vicinity of the magnetic phase transition.
