A review is given of an attempt, made in two recent papers, to estimate the gravitational action of faraway matter on a test particle, in connection with the velocity dispersion in clusters of galaxies and with the rotation curves of spiral galaxies, respectively. Under the assumptions that faraway matter has a fractal distribution and that the gravitational action has a correlation length of the order of some kiloparsec, the gravitational action of faraway matter appears to be sufficient to explain the observations relative to such two phenomena, without invoking any local, dark matter contribution.