New calculations of the Galactic contribution to microwave background radiation anisotropies are carried out and a probable Galactic predominance over cosmological signals at large scales is explored for these frequencies When we take into account a frequency-dependent contrast of molecular cloud with respect to the Galactic background of the diffuse interstellar medium, the anisotropic amplitude produced by Galactic dust is of the same order as that of the data from the observations. The frequency independence of anisotropies in the microwave range is not necessarily an argument against the Galactic predominance if we take into account an aditional rotational dust emission, for instance. This provides a basis for questioning the validity attributing a cosmological rather than a local origin for the greater part of the microwave background radiation anisotropies. Moreover, there is another strong evidence, which solves the question in favour of a Galactic predominance, to be shown in the conference.