The observed core-like distribution of the old stellar population of red giants near the massive black hole in the Galactic Center(GC)poses a challenge for theories of evolution of stellar population in galactic nuclei.The dynamical relaxation of such systems is expected to give rise to a steep(Bahcall-Wolf)power-law cusp n~r-7/4 distribution,inconsistent with the observations.Here we use Fokker-Planck calculations to study the effect of star formation on the evolution of the nuclear cluster stellar distribution.We show that the inclusion of several stellar populations,arising from star formation,could lead to the build up of a stellar core distribution of intermediate age stars(up to a few Gyrs old),similar to that observed for the red giants in the GC,while the older stellar population is relaxed in a typical cusp distribution.These results can reconcile the existence of an apparent core-like distribution,with the possible existence of an underlying cusp distribution for the old stellar population in the GC.distribution,inconsistent with the observations.Here we use Fokker-Planck calculations to study the effect of star formation on the evolution of the nuclear cluster stellar distribution.We show that the inclusion of several stellar populations,arising from star formation,could lead to the build up of a stellar core distribution of intermediate age stars(up to a few Gyrs old),similar to that observed for the red giants in the GC,while the older stellar population is relaxed in a typical cusp distribution.These results can reconcile the existence of an apparent core-like distribution,with the possible existence of an underlying cusp distribution for the old stellar population in the GC.