Abstract The high-temperature gas-cooled reactor (HTGR) appears as a good candidate for the next generation of nuclear power plants. In the “HTR-N” project of the European Union Fifth Framework Program, analyses have been performed on a number of conceptual HTGR designs, derived from reference pebble-bed and hexagonal block-type HTGR types. It is shown that several HTGR concepts are quite promising as systems for the incineration of plutonium and possibly minor actinides. These studies were mainly concerned with the investigation and intercomparison of the plutonium and actinide burning capabilities of a number of HTGR concepts and associated fuel cycles, with emphasis on the use of civil plutonium from spent LWR uranium fuel (first generation Pu) and from spent LWR MOX fuel (second generation Pu). Besides, the “HTR-N” project also included activities concerning the validation of computational tools and the qualification of models. Indeed, it is essential that validated analytical tools are available in the European nuclear community to perform conceptual design studies, industrial calculations (reload calculations and the associated core follow), safety analyses for licensing, etc., for new fuel cycles aiming at plutonium and minor actinide (MA) incineration/transmutation without multi-reprocessing of the discharged fuel. These validation and qualification activities have been centred round the two HTGR systems currently in operation, viz. the HTR-10 and the HTTR. The re-calculation of the HTTR first criticality with a Monte Carlo neutron transport code now yields acceptable correspondence with experimental data. Also calculations by 3D diffusion theory codes yield acceptable results. Special attention, however, has to be given to the modelling of neutron streaming effects. For the HTR-10 the analyses focused on first criticality, temperature coefficients and control rod worth. Also in these studies a good correspondence between calculation and experiment is observed for the 3D diffusion theory codes.