Single crystals of Bi2Sr2−xCuO6−y, (0.1 < x < 0.5, 0 < y < 0.5), were examined using x-ray diffraction techniques. Ditfractometer scans of θ-2θ taken normal to the cleavage planes displayed the even () reflections from = 2 to 26. Weak satellite peaks were observed on either side of each main () reflection, and their intensities relative to the main peak increased as 2θ was increased. With decreasing Sr content, the satellite peaks systematically moved away from the position of the main reflection. In contrast, the positions of the satellite peaks did not change with oxygen content which was varied by up to 0.5 oxygen atoms per formula unit. Since Tc in these crystals is sensitive to oxygen content while the superstructure modulation is not, it is unlikely that superconductivity and the structure modulation are directly related. As shown by a more detailed study of these peaks using a four-circle diffractometer and x-ray precession methods, the satellites that appear in θ-2θ scans are actually the mosaic tails of relatively intense superstructure peaks, positioned off from c* in the b* direction of reciprocal space. Depending on the Sr content of the crystals, generally incommensurate modulations were found with the superstructure periodicity ranging between ˜1/5b* + 0.29c* and ˜1/5b* + 0.65c*. The modulation in Bi2Sr2−xCuO6−y has two components. The component along the b* direction is similar to the superstructure observed in Bi2Sr2CaCu2O7 crystals and thus is probably due to the mismatch between the Bi2O2 layer and the CuO2 layer. The additional component along c* may be due to the ordering of Sr vacancies.