  Dynamo action in fully convective stars is a debated issue that also
questions our understanding of magnetic field generation in partly convective
Sun-like stars. During the past few years, spectropolari- metric observations
have demonstrated that fully convective objects are able to trigger strong
large-scale and long-lived magnetic fields. We present here the first
spectropolarimetric study of a sample of active late M dwarfs (M5-M8) carried
out with ESPaDOnS@CFHT. It reveals the co-existence of two distinct types of
magnetism among stars having similar masses and rotation rates. A possible
explanation for this unexpected discovery is the existence of two dynamo
branches in this parameter regime, we discuss here the possible identification
with the weak vs strong field bistability predicted for the geodynamo.
