We have developed a new model of evolutionary synthesis of stellar population, from a working cyclical approximation to a general solution for the mass and time dependence of the ‘birth function’ of stars. The general solution enables us to introduce a functionG(t): the ratio of gas injected into a defined region to that which forms stars in the same time interval, at timet. This function, by relating directly the output of dying stars with the formation of the next generation, allows us to make analytical approximations (in the absence of more accurate numerical information) to the macroscopic evolution of stellar populations in a well-defined zone of a galaxy.