The incentive of the Kernforschungszentrum Karlsruhe (KfK) advanced pressurized water reactor (APWR) investigations is the improvement of uranium utilization in a modem Federal Republic of Germany pressurized water reactor (PWR) by replacement of the core with a high converting one. The high conversion ratio is obtained by using mixed oxide (UPu)O2 in a tight light-water-moderated triangular lattice. The harder neutron spectrum leads to higher conversion ratios, to higher fissile enrichment and fissile inventories, and to worse reactivity behavior after coolant density changes. That means that core modification of the PWR shifts its neutron physics properties in the direction of fast reactor characteristics. The analysis of available calculational methods for fast and thermal reactors showed that neither the WIMS/D code, reliable for thermal reactors, nor the approved KAPROS fast reactor code can adequately predict the reactivity of an APWR in all configurations between normal and a totally voided core. A newly developed procedure, KARBUS, within the KAPROS fast reactor code system combines the advantageous features of thermal and fast reactor calculational methods. The preliminary validation for fast, epithermal, and thermal lattices, including burnup behavior, indicates that KARBUS is an adequate tool for the APWR investigations at present. Improvements in the detailed analysis of a final APWR design and of APWR neutron physics experiments in progress are briefly discussed. Parametric calculations for a simplified model indicate that current KfK proposals for homogeneous and heterogeneous APWR cores are nearly optimum concerning the competitive properties conversion ratio and void effect in a critical core poisoned by reactor control or by fission products.