A mathematical model of a detector has been constructed using the comparison of calculated and experimental values of the photon detection efficiency of a gamma spectrometer based on a high purity ger manium detector. The method and program for calculating the correction for coincidences in low activity measurements for radionuclides with complex decay schemes have been created. This study makes it possible to calculate the photon detection efficiency in the cases, where the working standards for the considered mea surement conditions are absent, and to take the correction of the experimental data for the cascade summa tion into account.