  We present in this paper the first results of a spectropolarimetric analysis
of a small sample (~ 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.
  The present paper focuses on 5 stars of spectral type ~M4, i.e. with masses
close to the full convection threshold (~ 0.35 Msun), and with short rotational
periods. Tomographic imaging techniques allow us to reconstruct the surface
magnetic topologies from the rotationally modulated time-series of circularly
polarised profiles. We fnd that all stars host mainly axisymmetric large-scale
poloidal fields. Three stars were observed at two different epochs separated by
~1 yr; we find the magnetic topologies to be globally stable on this timescale.
  We also provide an accurate estimation of the rotational period of all stars,
thus allowing us to start studying how rotation impacts the large-scale
magnetic field.
