We report on a theoretical study of the fine structure of excited excitonic levels in semiconductor quantum disks. A particular attention is paid to the effect of electron-hole long-range exchange interaction. We demonstrate that even in the axisymmetric quantum disks, the exciton P-shell is split into three subleveis. The analytical results are obtained in the limiting cases of strong and weak confinement. A possibility of exciton spin relaxation due to the resonant LO-phonon-assisted coupling between the P and S shells is discussed.