Optical harmonic generation on excitons is found in ZnSe/BeTe quantum wells with type-II band alignment. Two experimental approaches with spectrally-broad femtosecond laser pulses and spectrally-narrow picosecond pulses are used for spectroscopic studies by means of second and third harmonic generation (SHG and THG). The SHG signal is symmetry-forbidden for light propagation along the structure's growth axis, which is the [001] crystal axis, but can be induced by an external magnetic field. The THG signal is detected at zero magnetic field and its intensity is field independent. A group theory analysis of SHG and THG rotational anisotropy diagrams allows us to identify the involved excitation mechanisms.