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Previous models for the chemical evolution of the Magellanic Clouds have assumed either a steepened IMF compared to the solar neighbourhood or preferential expulsion of oxygen and α-particle elements by selective galactic winds. These assumptions were largely motivated by a belief that the O/Fe ratio in the Clouds is substantially lower than in the Galaxy, but the difference appears to have been exaggerated: Galactic supergiants have a similar O/Fe ratio as Cloud supergiants, there is no corresponding effect in Mg and other α-elements and a combination of data from planetary nebulae, H II regions and supernova remnants indicates an O/Fe ratio more or less equal to solar. Consequently new analytical models for the chemical evolution of the Magellanic Clouds have been developed, assuming chemical yields and time delays identical to those we previously assumed for the solar neighbourhood, but assuming (in addition to infall) non-selective galactic winds and burst-like modes of star formation represented by discontinuous variations in the star formation rate per unit gas mass. We find adequate agreement with age-metallicity relations and element:element ratios within their substantial uncertainties, whereas our LMC model turns out to give an excellent fit to the anomalous Galactic halo stars discovered by Nissen and Schuster (1997). It also gives an enhanced SNIa/SNII ratio compared to the solar neighbourhood, due to the assumption that the SFR has declined in the past 1 to 2 Gyr.