In situ STM images with atomic resolution of underpotentially deposition (upd) cadmium layers on Cu(1 1 1) and Cu(1 00) electrodes from a 10(-4) M CdCl2/10(-2) M HCl solution are presented. For the system CdCl2 on Cu(1 1 1) the observed long-range moire-like super structure is analysed by means of an algebraic model. A structure for the upd layer is developed and the height modulation for the Cd overlayer is reproduced by a hard-sphere model. This model fits remarkably well with the detailed tunnelling current density distribution of the measured STM images. Furthermore, we report the first in situ STM study of the Cd upd on Cu(1 0 0). The images show a stripe phase, the structure of which could be determined with atomic resolution. By means of these measurements a model for the detailed tunnelling current density distribution of the measured STM images, also as a function of bias voltage, is developed which leads to a (5root2 X root2)R45degrees-structure.