M dwarfs are the most numerous stars in our Galaxy with masses between approximately 0.5 and 0.1 solar mass. Many of them show surface activity qualitatively similar to our Sun and generate flares, high X-ray fluxes, and largescale magnetic fields 1-4 . Such activity is driven by a dynamo powered by the convective motions in their interiors 2,5-8 . Understanding properties of stellar magnetic fields in these stars finds a broad application in astrophysics, including, e.g., theory of stellar dynamos and environment conditions around planets that may be orbiting these stars. Most stars with convective envelopes follow a rotation-activity relationship where various activity indicators saturate in stars with rotation periods shorter than a few days 2,6,8 . The activity gradually declines with rotation rate in stars rotating more slowly. It is thought that due to a tight empirical correlation between X-ray and magnetic flux 9 , the stellar magnetic fields will also saturate, to values around ∼ 4 kG 10 . Here we report the detection of magnetic fields above the presumed saturation limit in four fully convective M-dwarfs. By combining results from spectroscopic and polarimetric studies we explain our findings in terms of bistable dynamo models 11,12 : stars with the strongest magnetic fields are those in a dipole dynamo state, while stars in a multipole state cannot generate fields stronger than about four kilogauss. Our study provides observational evidence that dynamo in fully convective M dwarfs generates magnetic fields that can differ not only in the geometry of their large scale component, but also in the total magnetic energy.Our understanding of origin and evolution of the magnetic fields in M dwarfs is based on the models of the rotationally driven convective dynamos. Modern observations provide two important constraints for these models.First, from the analysis of circular polarization in spectral lines we infer that large-scale magnetic fields tend to have simple axisymmetric geometry with dominant poloidal component in stars that are fully convective. In contrast, M dwarfs that are hotter and therefore only 1 arXiv:1801.08571v1 [astro-ph.SR] 25 Jan 2018 partly convective tend to have more complex fields with strong toroidal components 13 . However, there is a number of exceptions when a rapidly-rotating fully convective star generates a large-scale magnetic field with a complex multipole geometry. This dichotomy of magnetic properties in stars that have similar stellar parameters may be explained in terms of dynamo bistability: stars can relax to either dipole or multipole states depending on the geometry and the amplitude of an initial seed magnetic field 11,12 . Note, however, that dynamo bistability was observed only in models of stars with masses M 0.2M .The second observational constraint is the rotation-activity relation 2,8,14,15 . A remarkable feature of this relation is the existence of two branches, a saturated and a non-saturated branch. In the non-saturated branch, the amount of non-thermal (e.g...