The high field phenomena of inter-valley transfer and avalanching breakdown have long been exploited in devices based on conventional semiconductors. In this Article, we demonstrate the manifestation of these effects in atomically-thin WS field-effect transistors. The negative differential conductance exhibits all of the features familiar from discussions of this phenomenon in bulk semiconductors, including hysteresis in the transistor characteristics and increased noise that is indicative of travelling high-field domains. It is also found to be sensitive to thermal annealing, a result that we attribute to the influence of strain on the energy separation of the different valleys involved in hot-electron transfer. This idea is supported by the results of ensemble Monte Carlo simulations, which highlight the sensitivity of the negative differential conductance to the equilibrium populations of the different valleys. At high drain currents (>10 μA/μm) avalanching breakdown is also observed, and is attributed to trap-assisted inverse Auger scattering. This mechanism is not normally relevant in conventional semiconductors, but is possible in WS due to the narrow width of its energy bands. The various results presented here suggest that WS exhibits strong potential for use in hot-electron devices, including compact high-frequency sources and photonic detectors.