The reactor physics problems in core designs for high-burnup and long-operating-cycle length are clarified. Two core concepts are proposed to deal with these problems: 1. the advanced homogeneous core (A-HOC) in which the power distribution is flattened by dividing the core into two regions with different fuel volume fractions 2. the advanced axial heterogeneous core (A-AHC) in which a thin internal blanket is introduced at the core midplane in the inner core region of the A-HOC. Core performance parameters such as fissile inventory, breeding ratio, and power and flux distributions are evaluated in detail by discrete burnup analyses. The results show that the A-AHC has more uniform power and flux distributions and a more stable power shape than the A-HOC, and the A-AHC seems to be a good candidate for achieving high-burnup and long-operating-cycle length.