Multiple frequency quantum beats of a system of the coherently excited quantum confined exciton states in a high-quality semiconductor structure containing a wide InGaAs/GaAs quantum well are experimentally detected by the spectrally resolved pump-probe method. The beat signal is observed both at positive and at negative delays between the pump and probe pulses. Several quantum beat (QB) frequencies are observed in the experiments, which coincide with the interlevel spacings in the exciton system. A theoretical model is developed, which allows one to attribute the QBs at negative delay to the four-wave mixing (FWM) signal detected at the nonstandard direction. The beat signal is strongly enhanced by the interference of theFWMsignal with the secondary emission induced by the probe pulse. At positive delays, the QBs are due to the interference of the quantum confined exciton states. The decay time for QBs is of the order of several picoseconds both at positive and negative delays. This is close to the relaxatio