The optical coherent-control technique is used to study biexcitonic effects in the four-wave-mixing signal of a ZnSe single quantum well. The signal is analyzed in both directions 2k 1 À k 2 and 2k 2 À k 1 which are not equivalent if a pulse pair is applied from direction k 1 to achieve coherent control of the induced polarization. It is shown that the coherent control enables a selective enhancement or suppression of the contribution at the exciton and biexciton resonance to the signal, respectively, but only for certain sequences of the excitation pulses. Further, the suppression of exciton-biexciton beats in the signal as a function of t del by a selective destruction of the biexciton polarization is demonstrated.1 Introduction Optical coherent-control techniques have been widely used in the last few years since they offer the possibility to manipulate quantum-mechanical excitations with regard to both their amplitudes and relative phases [1][2][3]. The control can be achieved by generating a collinear pair of laser pulses with a relative phase being tuneable with a resolution of just a fraction of the excitation wavelength [4][5][6]. This method offers the possibility to switch continuously between destructive and constructive interference for different excitations in the sample [7]. Thus, optical coherent control provides an outstanding technique to separate between certain spectral contributions in the signal by selectively exciting only one or just a few resonances in the sample. Clearly, this argument holds for all systems containing resonances which are not coupled to each other. In the case of exciton and biexciton polarization, however, one has to deal with two resonances which are strongly coupled since a bound biexciton is composed of two excitons with opposite spins. Because of this it is not a priori clear whether the excitonic and biexcitonic contributions in a four-wave-mixing signal can be separated by applying an optical coherent-control technique. Recently, we have shown the separate coherent control of exciton and biexciton four-wave-mixing polarization by observing a phase shift between the signals at the two resonances corresponding to their energenic separation [8]. Here, we extend this work to a more general case where different sequences of the excitation pulses are used and the resulting four-wave-mixing signals are studied spectrally resolved in both directions 2k 1 À k 2 and 2k 2 À k 1 as a function of the delay time t del .