The β Cephei instability is believed to be caused by the κ-mechanism. Model calculations, based on revised metal opacities, show this mechanism to be strongly sensitive to metallicity (e.g., Dziembowski, W. A. & Pamyatnykh, A. A., 1993: MNRAS, 262, 204). It appears that [Fe/H] must be larger than the solar value in order to drive the β Cephei pulsations. For this reason, the models predict that no β Cephei stars should be found in the Magellanic Clouds. Balona (1992: MNRAS, 256, 425; 1992: ASP Conf. Ser., Vol. 30, 155; 1993: MNRAS, 260, 795) has tested this prediction by observing three young clusters in the SMC and LMC (NGC 330, NGC 2004 and NGC 2100). He found no β Cephei stars down to a magnitude of V ≈ 16; the threshold for detection of variability on time-scales of a few hours was 10 mmag. Most Galactic β Cephei stars have amplitudes greater than this, but we might expect β Cephei stars in the Magellanic Clouds (if they exist) to have smaller amplitudes, due to the different environment. To test this, we have observed two young clusters NGC 371 (SMC) and NGC 2122 (LMC) with high sensitivity.