  We discuss the grazing collision limit of certain kinetic models of
Bose-Einstein particles obtained from a suitable modification of the one-
dimensional Kac caricature of a Maxwellian gas without cut-off. We recover in
the limit a nonlinear Fokker-Planck equation which presents many similarities
with the one introduced by Kaniadakis and Quarati in [13 ]. In order to do so,
we perform a study of the moments of the solution. Moreover, as is typical in
Maxwell models, we make an essential use of the Fourier version of the
equation.
