Boron neutron capture therapy, BNCT, might be a valuable tumour therapeutical modality for the treatment of cells that are difficult to handle with conventional methods such as surgery or external radiotherapy. The principle is that tumour associated B-10 atoms capture thermal neutrons and thereby forms high-LET helium and lithium ions as reaction products. An interesting development is to conjugate B-10 atoms to macromolecules that bind to tumour cells with over-expressed receptors or specific antigens. The targeting macromolecules might be receptor-ligands, antibodies or antibody-fragments containing B-10. The present study deals with the limitations of such an approach. One problem is the background dose from capture of neutrons in physiologically occurring elements, especially nitrogen. We showed, with computer simulations, that the background specific energy (the stochastic analogy of dose) in the cell nuclei, due to captures in nitrogen, had a wide spread and could be rather high, up to 3 Gy in some cells, when relevant neutron fluencies were applied. The maximal amount of B-10 that can be delivered to single tumour cells due to receptor-ligand, receptor-antibody or antigen-antibody mediated binding is probably in the range 10(8)-10(10) atoms/cell. Our calculations showed that the tumour cells had to. contain about 10(9) B-10/cell to give a therapeutically interesting dose to the nuclei of the targeted cells. The doses were highest when the boron was in the cell nucleus. There was also a wide spread of specific energy absorbed by the nuclei after neutron capture in B-10. When, for example, (10)8 10(10)Binucleus were applied the specific energy to the analysed nuclei varied from 0 Gy up to about 7 Gy. These variations were due to the stochastic nature of the capture processes. Some helium or lithium ion tracks passed through the centre of the cell nuclei delivering a lot of energy, some passed through only a smaller part delivering small amounts of energy and sometimes the nuclei escaped without any hits at all. The results were obtained when relevant neutron fluencies (2-5 x 10(12) n/cm(2)) were applied. Increased neutron fluencies gave higher doses both due to capture in boron and in nitrogen but in order to improve the ratio between the dose to targeted tumour cells and the dose to normal cells, the number of B-10 atoms in the targeted cells had to be increased and/or the boron placed in the cell nuclei.