  Dust emission at submm to cm wavelengths is often simply the Rayleigh-Jeans
tail of dust particles at thermal equilibrium and is used as a cold mass tracer
in various environments including nearby galaxies. However, well-sampled
spectral energy distributions of the nearby, star-forming Magellanic Clouds
have a pronounced (sub-)millimeter excess (Israel et al., 2010). This study
attempts to confirm the existence of such a millimeter excess above expected
dust, free-free and synchrotron emission and to explore different possibilities
for its origin. We model NIR to radio spectral energy distributions of the
Magellanic Clouds with dust, free-free and synchrotron emission. A millimeter
excess emission is confirmed above these components and its spectral shape and
intensity are analysed in light of different scenarios: very cold dust, Cosmic
Microwave Background (CMB) fluctuations, a change of the dust spectral index
and spinning dust emission. We show that very cold dust or CMB fluctuations are
very unlikely explanations for the observed excess in these two galaxies. The
excess in the LMC can be satisfactorily explained either by a change of the
spectral index due to intrinsic properties of amorphous grains, or by spinning
dust emission. In the SMC however, due to the importance of the excess, the
dust grain model including TLS/DCD effects cannot reproduce the observed
emission in a simple way. A possible solution was achieved with spinning dust
emission, but many assumptions on the physical state of the interstellar medium
had to be made. Further studies, using higher resolution data from Planck and
Herschel, are needed to probe the origin of this observed submm-cm excess more
definitely. Our study shows that the different possible origins will be best
distinguished where the excess is the highest, as is the case in the SMC.
