  We present here the first results of a spectropolarimetric analysis of a
small sample (about 20) of active stars ranging from spectral type M0 to M8,
which are either fully-convective or possess a very small radiative core. This
study aims at providing new constraints on dynamo processes in fully-convective
stars.
  Results for stars with spectral types M0-M4 -- i.e. with masses above or just
below the full convection threshold (about 0.35Msun) -- are presented.
Tomographic imaging techniques allow us to reconstruct the surface magnetic
topologies from the rotationally modulated time-series of circularly polarised
profiles.
  We find strong differences between partly and fully convective stars
concerning magnetic field topology and characteristic scales, and differential
rotation. Our results suggest that magnetic field generation in fully
convective stars relies on different dynamo processes than those acting in the
Sun and other partly convective stars, in agreement with theoretical
expectations.
