Context : Massive binaries have stellar winds that collide .
In the colliding-wind region , various physically interesting processes occur , leading to enhanced X-ray emission , non-thermal radio emission , as well as non-thermal X-rays and gamma-rays .
Non-thermal radio emission ( due to synchrotron radiation ) has so far been observed at centimetre wavelengths .
At millimetre wavelengths , the stellar winds and the colliding-wind region emit more thermal free-free radiation , and it is expected that any non-thermal contribution will be difficult or impossible to detect .

Aims : We aim to determine if the material in the colliding-wind region contributes substantially to the observed millimetre fluxes of a colliding-wind binary .
We also try to distinguish the synchrotron emission from the free-free emission .

Methods : We monitored the massive binary Cyg~OB2~ # 8A at 3 mm with the NOrthern Extended Millimeter Array ( NOEMA ) interferometer of the Institut de Radioastronomie Millimétrique ( IRAM ) .
The data were collected in 14 separate observing runs ( in 2014 and 2016 ) , and provide good coverage of the orbital period .

Results : The observed millimetre fluxes range between 1.1 and 2.3 mJy , and show phase-locked variability , clearly indicating that a large part of the emission is due to the colliding-wind region .
A simple synchrotron model gives fluxes with the correct order of magnitude , but with a maximum that is phase-shifted with respect to the observations .
Qualitatively this phase shift can be explained by our neglect of orbital motion on the shape of the colliding-wind region .
A model using only free-free emission results in only a slightly worse explanation of the observations .
Additionally , on the map of our observations we also detect the O6.5 III star Cyg~OB2~ # 8B , for which we determine a 3 mm flux of 0.21 \pm 0.033 mJy .

Conclusions : The question of whether synchrotron radiation or free-free emission dominates the millimetre fluxes of Cyg~OB2~ # 8A remains open .
More detailed modelling of this system , based on solving the hydrodynamical equations , is required to give a definite answer .