Certain aspects of the AGB population, such as the relative number of M and N stars, the mass loss rates, and the initial masses of carbon-oxygen cores, depend on the initial heavy element abundance Z. I have calculated synthetic populations of AGB stars for different initial Z values taking into consideration the evolution of single and close binary stars. I present the results of population syntheses of AGB stars in clusters as a function of different initial chemical compositions. The relation for the tip luminosity of AGB stars versus cluster age as a function of Z is presented and is used to determine the ages for a number of clusters in the LMC and the SMC, including clusters with no previous age determinations.