[en] We have used inelastic neutron scattering to determine the spin dynamics in the Kondo insulator CeNiSn under magnetic fields up to 10 T applied parallel to the easy a axis. The well known excitations peaked at (h/2π)ω = 2 meV located at the Brillouin zone centre and at (h/2π)ω = 4 meV located at the Brillouin zone border were studied comparatively. At the scattering vectors (0 1 0) and (0 0 1) the peak shifts continuously from 2 to 2.5 meV with the field. No Zeeman splitting could be detected at the accuracy of our measurements. For the '4 meV' excitation studied at the scattering vector (0 0.5 1), a field as large as 10 T begins to fill in the gap whereas there is no appreciable change in the spin dynamics between 0 and 6 T. The main feature is the broadening of the response. We compare our experimental results to recent theoretical developments. (author)