The calculation of excited states in multicomponent systems, in which more than one type of particle is described quantum mechanically, is important for a wide range of applications in chemistry and physics. The nuclear-electronic orbital (NEO) approach has been used to treat all electrons and key protons, or the positron for positronic systems, quantum mechanically on the same level with density functional theory or wavefunction-based methods. The NEO coupled cluster singles and doubles (NEO-CCSD) method has been shown to provide accurate densities, energies, and optimized geometries for multicomponent systems. Herein, the multicomponent equation-of-motion CCSD (NEO-EOM-CCSD) method is developed for the calculation of excitation energies in multicomponent systems. The working equations are derived and implemented, and the programmable equations are provided to enable others to implement this method. This approach is validated by the comparison of the ground state and first three excited state energies of positronium hydride computed with the NEO-EOM-CCSD method to the values calculated with the NEO full configuration interaction and full coupled cluster methods. The development of the NEO-EOM-CCSD method paves the way for a wide range of applications in excited state multicomponent quantum chemistry.