A method is presented for obtaining the tracks of evolution for individual stars in the subgiant and giant regions of color-magnitude diagrams of star clusters. The method utilizes the evolutionary information contained in the observed luminosity functions and color-magnitude diagrams of clusters. It is applied to the galactic cluster M67 and to the globular cluster M3. The evolutionary tracks, the time scale for evolution along these tracks, and the fraction of the total mass exhausted of hydrogen have been computed for both clusters, and the results are tabulated in Tables 3-10. The computed fraction of the mass exhausted of hydrogen for stars in M3 is compared with the theoretical predictions of the HoyleSchwarzschild (H-S) models. Fair agreemenL is obtained It is shown that the H-S models are capable of predicting nearly the correct luminosity function for M3 except at the very top of the giant sequence. The time taken for stars to evolve along the horizontal branch in M3 from B - V = 0.50 to B - V = -0.10 is found to be 2 3 X 108 years. The lifetime of the RR Lyrae phase of the evolution is 8 X 10 years. The expected rate of change of the period of the RR Lyrae stars due to this evolution is At/t = 2.4 X 10-li, or 0.1 second per century, which is about a factor of 5 below the limit of detectability with the available data. The observed period changes for RR Lyrae stars in M3 average twenty times this value and are believed to be due to causes other than evolution.