Summary form only given. Brillouin fiber ring lasers have already been extensively studied and results have shown that the generated first order Stokes wave has less intensity and phase noise than the seeded pump. This increase in coherence is attractive for many sensing applications, whether in the field of fiber sensors or remote sensing systems such as LIDAR. Brillouin fiber lasers with several Stokes components can further increase the coherence through a cascading effect, the 1st Stokes component being the pump for the 2nd Stokes order and so on. In this communication, we investigate the noise properties of a multi-Stokes Brillouin fiber laser. We present numerical simulations from a model that is an extension of the usual three-waves model of stimulated Brillouin scattering in agreement with experimental results.