The exciton binding energy in GaAs-based quantum-well (QW) structures is in the range of ∼10 meV, which falls in the THz regime. We have conducted a time-resolved study to observe the resonant interactions of strong narrowband THz pulses with coherent excitons in QWs, where the THz radiation is tuned near the 1s-2p intraexciton transition and the THz pulse duration (∼3 ps) is comparable with the exciton dephasing time. The system of interest contains ten highquality 12-nm-wide GaAs QWs separated by 16-nm-wide Al 0.3Ga 0.7As barriers. The strong and narrowband THz pulses were generated by two linearly-chirped and orthogonally-polarized optical pulses via type-II difference-frequency generation in a 1-mm ZnTe crystal. The peak amplitude of the THz fields reached ∼10 kV/cm. The strong THz fields coupled the 1s and 2p exciton states, producing nonstationary dressed states. An ultrafast optical probe was employed to observe the time-evolution of the dressed states of the 1s exciton level. The experimental observations show clear signs of strong coupling between THz light and excitons and subsequent ultrafast dynamics of excitonic quantum coherence. As a consequence, we demonstrate frequency conversion between optical and THz pulses induced by nonlinear interactions of the THz pulses with excitons in semiconductor QWs.