By their star content, the galaxies split out into a red and a blue population; their color index peaked around u-r ≈ 2.5 or u-r ≈ 1, respectively, quantifies the ratio of the blue stars newly formed from cold galactic gas, to the redder ones left over by past generations. On the other hand, on accreting substantial gas amounts the central massive black holes energize active galactic nuclei (AGNs); here we investigate whether these show a similar, and possibly related, bimodal partition as for current accretion activity relative to the past. To this aim we use an updated semianalytic model; based on Monte Carlo simulations, this follows with a large statistics the galaxy assemblage, the star generations, and the black hole accretions in the cosmological framework over the redshift span from z = 10 to z = 0. We test our simulations for yielding in close detail the observed split of galaxies into a red, early and a blue, late population. We find that the black hole accretion activities likewise give rise to two source populations: early, bright quasars and later, dimmer AGNs. We predict for their Eddington parameter λE—the ratio of the current to the past black hole accretions—a bimodal distribution; the two branches sit now under λE ≈ 0.01 (mainly contributed by low-luminosity AGNs) and around λE ≈ 0.3-1. These not only mark out the two populations of AGNs, but also will turn out to correlate strongly with the red or blue color of their host galaxies.