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In this work, we present the results of a novel approach devoted to disentangling the role of the environmental processes affecting galaxies in clusters. This is based on the analysis of the near-UV (NUV) - r' distributions of a large sample of star-forming galaxies in clusters spanning more than four absolute magnitudes. The galaxies inhabit three distinct environmental regions: virial regions, cluster infall regions, and field environment. We have applied rigorous statistical tests to analyze both the complete NUV - r' distributions and their averages for three different bins of the r'-band galaxy luminosity down to M-r' similar to -18, throughout the three environmental regions considered. We have identified the environmental processes that significantly affect the star-forming galaxies in a given luminosity bin by using criteria based on the characteristics of these processes: their typical timescales, the regions where they operate, and the galaxy luminosity range for w! hich their effects are more intense. We have found that the high-luminosity (M-r' <= -20) star-forming galaxies do not show significant signs in their star formation activity of being affected by: (1) the environment in the last similar to 10(8) yr, or (2) a sudden quenching in the last 1.5 Gyr. The intermediate-luminosity (-20 < M-r' <= -19) star-forming galaxies appear to be affected by starvation in the virial regions and by the harassment in the virial and infall regions. Low-luminosity (-19 < M-r' <= -18.2) star-forming galaxies seem to be affected by the same environmental processes as intermediate-luminosity star-forming galaxies in a stronger way, which would be expected for their lower luminosities.