Abstract.: In this paper we consider the magnetic Couette-Taylor problem, that is, a conducting fluid between two infinite rotating cylinders, subject to a magnetic field parallel to the rotation axis. This configuration admits an equilibrium solution of the form (0,ar+br−1,0,0,0,α+βlogr). It is shown that this equilibrium is Ljapounov stable under small perturbations in L2(Γ), where Γ={(r,φ,z)/r1<r<r2,φ∈[0,2π],z∈R}, provided that the parameters a, b, α, β are small. The methods of proof are a combination of an energy method, based on Bloch space analysis and small data technique
