We consider Raman ring laser by modeling the laser pump light by a classical time-dependent random process, namely a pre-Gaussian process. It is composed of a finite number of independent so-called telegraphs. The strength of the pre-Gaussian formalism derives from the exact solubility of wide classes of the stochastic equations. In particular we also observed the so-called noise reduction in Raman ring laser: the Stokes output of this laser tends to the stabilize under the influence of the broad-band one-telegraph pre-Gaussian pump (Cao Long and Doan Quoc in Opt Quant Electron 43:137–145, 2012). We extend our model to the case of two-telegraph pre-Gaussian noise and compare obtained results with that obtained in our previous paper for the case of broad-band one-telegraph pre-Gaussian pump.