Period-luminosity relations are derived in 0, 0, 0 and 0 for 21 Galactic calibrating Cepheids, together with 115 Cepheids in the Magellanic Clouds. Period- colour relations are derived for 0 - 0, 0 - 0 and 0 - 0, and colour- colour relations between 0 - 0 and 0 - 0 for various samples of Cepheids with known optical and/or infrared colours. Zero-point shifts in these relations are used together with the model colours of Bell & Gustafsson to determine the bolometric corrections involved in calculating the distance moduli of the Magellanic Clouds. With a Pleiades distance modulus of 5.57, we find the distance moduli of the LMC and SMC to be 18.53 and 18.94, with internal standard errors of 0.04. If calibrators in associations are given half-weight, these moduli diminish by about 0.04. The available data cannot be reconciled with the hypothesis that period-luminosity and/or period-colour relations are independent of metallicity for all wavelengths.