The method of calculating dose factors for the haemopoitic marrow and endosteal tissues in human trabecular bone, used by Whitwell and Spiers for volume-seeking radionuclides, has been developed for the case of radionuclides which are deposited as very thin layers on bone surfaces. The Monte Carlo method is again used, but modifications to the computer program are made to allow for a surface rather than a volume source of particle emission. The principal change is the introduction of a surface-orientation factor which is shown to have a value of approximately 2, varying slightly with bone structure. Result are given for beta-emitting radionuclides ranging from 171Tm (E (E beta=0.025 MeV) to 90Y(E beta = 0.93MeV), and also for the alpha-emitter 239Pu. It is shown that where the particle ranges are short compared with the dimensions of the bone structures the dose factors for the surface seekers are much greater than those for the volume seekers. For long range particles the dose factors for surface and volume-seeking radionuclides converge. Comparisons are given relating the dose factors calculated in this paper on the basis of measured bone structures to those of other workers based on single plane geometry.