<p>A population forecast is a projection in which fertility should involve both women and men. However, in demography, fertility refers to the number of children born to women, the linear renewal model includes only one sex, and the population projections regularly issued by the Governments are female renewal of which only women produce births. A major reason for the absence of men is there was no two-sex renewal model that could be used for population projection. Such a model was published recently. Accordingly, two-sex renewal population projections can be calculated, and the projected annual births are observed to always change exponentially with damped waves. Are the observations common? This fundamental question was not answered, because the renewal model is nonlinear and its general solution was unknown. Assuming maternal and paternal ages are independent, the general solution of the two-sex renewal model is obtained and the fundamental question is answered. The births changing exponentially with damped waves would be common, and sensitivity and chaos could be precluded from two-sex renewal population projections. Furthermore, the general solution indicates that female-renewal population projection cannot correctly calculate two-sex population changes. Using the general solution and data from Japan and the US, examples of extending population momentum and stable population to two sexes are provided. The damped waves are explained, and the assumption of independent maternal and paternal ages is examined.</p>