Period, luminosity and colour data on LMC and SMC Cepheids are analysed. A geometrical model for the LMC and the SMC is presented based on the Cepheids. The distance modulus of each Cloud is redetermined and its dependence upon the assumed abundance deficiency in the Clouds is made explicit. New, independent abundances are inferred based on the Cepheids alone, and are found to agree well with the known HII region abundance deficiencies. The luminosity laws in both galaxies, suitably corrected for abundance, are mutually consistent, enabling a 'universal' PLC and PL relation to be obtained which incorporates all the photoelectric data. (author).