In a number of recent experiments on the pure CeB6 compound, we have revealed strong quasielastic inten-sity in the normal (paramagnetic) state with a rich momentum-space structure. Below the antiferromagnetic (AFM) transition temperature, TN = 2.3K, this intensity gave rise to sharp collective modes. Under the influence of La doping, these modes were shown to change drastically. They vanished completely near 28% La concentra-tion, transforming into a purely quasielastic signal in zero field. Here we suggest to map out the dispersion of such low-energy modes in two single crystals with different La concentrations, 23% and 28%, to understand the changes in the magnetic intensity distribution with respect to the parent compound.