The exciton mode in the superconductor as a bound pair of quasi- particles whose center-ofmass propagates with a certain momentum is discussed. The exciton spectrum is investigated through generalized equations of motion involving the quasi-particle operators of Bogoliubov and Valatin rather than ck, the usual electron operators. In these equations an expansion of the interaction potential in terms of spherical harmonics is presented. It is found that excitons may be characterized by the approximate quantum numbers L and M describing the symmetry of the states with respect to the relative coordinates. The existence of an L-state exciton corresponding to the p,d,f,...excitons is dependent on VL being negative, where VL is the L-wave part of the interaction potential. The plasmon state corresponds to an s-state exciton whose energy is greatly increased by the long-range Coulomb interaction.