Classical adiabatic stability criteria appear to be pessimistic for multifilamentary composites. The thermal conductivity K, the magnetic and thermal diffusivities Dmand Dθ, the heat transfer coefficient hkplay a leading part in the determination of a stable composite. The differential magnetic and thermal equations have been solved and typical stability curves are given for either the slab model or the round conductor. Measurements of the quenching currents, in different magnetic, thermal and cooling conditions, for two meter long non inductive coils are made. The results are in good agreement with the theoretical predictions.