We have identified excited exciton states in monolayers of MoS₂ and WS₂ supported on fused silica by means of photoluminescence excitation spectroscopy. In monolayer WS₂, the positions of the excited A exciton states imply an exciton binding energy of 0.32 eV. In monolayer MoS₂, excited exciton transitions are observed at energies of 2.24 and 2.34 eV. Assigning these states to the B exciton Rydberg series yields an exciton binding energy of 0.44 eV.