  Context. Particle-accelerating colliding-wind binaries (PACWBs) are systems
that are formed by two massive and hot stars and produce nonthermal (NT)
radiation. The key elements of these systems are fast winds and the shocks that
they create when they collide. Binaries with nonaccreting young pulsars have
also been detected as NT emitters, again as a consequence of the wind-wind
interaction. Black holes (BHs) might produce NT radiation by this mechanism if
they accrete at super-Eddington rates. In such cases, the disk is expected to
launch a radiation-driven wind, and if this wind has an equatorial component,
it can collide with the companion star yielding a PACWB. These systems are
supercritical colliding wind binaries (SCWBs).
  Aims. We aim to characterize the particle acceleration and NT radiation
produced by the collision of winds in binary systems composed of a
superaccreting BH and an early-type star.
  Methods. We estimated the terminal velocity of the disk-driven wind by
calculating the spatial distribution of the radiation fields and their effect
on disk particles. We then found the location of the wind collision region and
calculated the timescales of energy gain and losses of relativistic particles
undergoing diffusive acceleration. With this information, we were able to
compute the associated spectral energy distribution of the radiation.
  Results. We find that the interaction of winds can produce NT emission from
radio up to tens of GeV, with luminosities in the range of $\sim
10^{33}-10^{35} \, {\rm erg \, s^{-1}}$, which for the most part are
contributed by electron synchrotron and inverse Compton radiation.
  Conclusions. We conclude that SCWBs, such as some ultraluminous X-ray sources
and some Galactic X-ray binaries, are capable of accelerating cosmic rays and
producing NT electromagnetic emission from radio to $\gamma$-rays, in addition
to the thermal components.
