The magnetic inelastic scattering of neutrons by paramagnetic media with exchange interactions has been studied, using the time-dependent spin correlation functions introduced by V an H ove. It is found that the even moments of the energy transfer depend strongly on momentum transfer (for small momentum transfer, all moments go to zero), and on the state of the scatterer (single crystal or powder). The shape and half-width of the spectrum are given as functions of the scattering angle for a polycrystàl with nearest-neighbour interactions. The whole study has been confined to the high-temperature region.