The Raman spectra of NiS$_{2-x}$Se$_x$ ($0 < x < 2$) polycrystalline thin films have been measured for the first time in the whole $x$ range and for NiSe$_2$. The NiSe$_2$ spectrum is qualitatively similar to the spectrum of NiS$2$, but all frequencies are shifted to lower energies. The shift has been analysed in terms of the increment of the anion mass and the lattice expansion. Peaks in the Raman spectrum of the NiS${2-x}$Se$_x$ alloy can be assigned to stretching and rotational modes of the S-S, Se-Se and S-Se pairs. The stretching vibration of the S-Se pairs shifts almost linearly from 400 cm$^{-1}$ for NiS$_2$ to 330 cm$^{-1}$ for NiSe$_2$. There is an accidental degeneracy between the S-S stretching and Se-Se libration frequencies. The relative Raman intensities fit well with a random occupation of the anion sites by S and Se atoms, and different scattering cross sections.