When plasmonic excitations of metallic interfaces and nanostructures interact with electronic excitations in semiconductors, new states emerge that hybridize the characteristics of the uncoupled states. The engendered properties make these hybrid states appealing for a broad range of applications, ranging from photovoltaic devices to integrated circuitry for quantum devices. Here, through quantum modeling, the coupling of surface plasmon polaritons and mobile two-dimensional excitons such as those in atomically thin semiconductors is examined with emphasis on the case of strong coupling. Our model shows that at around the energy crossing of the dispersion relationships of the uncoupled species, they strongly interact and polariton states-propagating plexcitons-emerge. The temporal evolution of the system where surface plasmon polaritons are continuously injected into the system is simulated to gain initial insight on potential experimental realizations of these states. The results show a steady state that is dominated by the lower-energy polariton. The study theoretically further establishes the possible existence of propagating plexcitons in atomically thin semiconductors and provides important guidance for the experimental detection and characterization of such states for a wide range of optoelectronic technologies.