For a modified version of the anthropoid MIRD phantom the organ doses and the effective dose equivalent for external neutron irradiation have been calculated in the past by the so called CHORD method. It was anticipated from a few preliminary Monte Carlo Calculations and based upon basic physical considerations that CHORD results may be generally too high in the case of organs positioned on the exit side of radiation, especially for the smaller head and neck part of the phantom. To prove this, extensive calculations have been performed with the Monte Carlo code SAM-CE for a male and a female phatom and the results of both calculations have been intercompared. In addition, organ doses were derived by the CHORD method for gamma irradiation, and have been compared with Monte Carlo calculations by other authors. The deviations are discussed with respect to their relevance for the determination of the primary limited quantities and with respect to the economy of the calculations.