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The majority of close massive binary stars with initial periods of a few daysexperience a contact phase, in which both stars overflow their Roche lobessimultaneously. We perform the first dedicated study of the evolution ofmassive contact binaries and provide a comprehensive prediction of theirobserved properties. We compute 2790 detailed binary models for the Large andSmall Magellanic Clouds each, assuming a conservative mass transfer. Theinitial parameter space for both grids span total masses from 20 to80$\,\textrm{M}_{\odot}$, orbital periods of 0.6 to 2 days and mass ratios of0.6 to 1.0. We find that models that remain in contact over nuclear timescalesevolve towards equal masses, echoing the mass ratios of their observedcounterparts. Ultimately, the fate of our nuclear-timescale models is to mergeon the main sequence. Our predicted period-mass ratio distributions of O-typecontact binaries are similar for both galaxies, and we expect 10 such systemstogether in both Magellanic Clouds. While we can largely reproduce the observeddistribution, we over-estimate the population of equal-mass contact binaries.This situation is somewhat remedied if we also account for binaries that areapproaching contact. Our theoretical distributions work particularly well forcontact binaries with periods $<$2 days and total masses$\lessapprox45\,\textrm{M}_{\odot}$. We expect stellar winds, non-conservativemass transfer and envelope inflation to have played a role in the formation ofthe more massive and longer-period contact binaries.

Detailed evolutionary models of massive contact binaries: I. Model grids and synthetic populations for the Magellanic Clouds