This paper proposes a new model for population projections. This model projects an initial population under conditions of fertility, mortality, and international migration (like standard cohort-component models), but considers the population arrayed by generation. The model incorporates 4 generations: a foreign-born first generation (the immigrants), a second generation (sons and daughters of immigrants), a third generation (grandsons and granddaughters of immigrants), and fourth-and-higher generations. The model requires fertility, mortality, and migration equations by generation, which take a somewhat different form than in conventional cohort-component population projection. Consideration of the model also makes apparent that assignment of births to generations may not follow a simple form: the paper presents a method for including the empirical description of intergenerational births within the generational framework. As an example, the authors examine the next century of population growth for the Asian, Black, Hispanic, and White non-Hispanic populations in the US, comparing their growth rates and their composition within the total US population. With annual net immigration of 950,000, the total US population of 249 million in 1990 will top 400 million in 2070 and reach about 432 million in 2090. Thus, the level of immigration and emigration assumed in these projections suggests considerable population growth for the next hundred years. The racial/ethnic composition of the US will shift markedly during the next century, as described in the paper.