By applying population synthesis method, stellar populations in the nuclei of M31 and M32 are studied. We obtained five and four models for M31 and M32 respectively, for different main sequence turn-offs and keeping the astrophysical constraints as loose as possible. The best models for M31 and M32 are thought to have G0-5 and F5-8 main sequence trun-offs respectively. These models show that the main sequence stars outnumber the giants, which indicates the dwarf-dominance in external galactic nuclei. Even though there are some computational difficulties because of non-uniqueness in solution, two major points can be pointed out when compared to the previous papers. First, the ultraviolet deficiency expected from the conventional metal rich population models is not detected in our models, Instead ultraviolet radiation turns out to be somewhat higher than that of observation. Second one is the minor contribution from the Super Metal Rich (SMR) K giants to the integrated light of the program galaxies. That is, in our models, the SMR contribution is at best the same level as normal giants contrary to the SMR dominance of previous models. Since the loose astrophysical constraints are the major difference of our study from the previous ones, one should re-examine carefully for their validity further.