This discussion which is restricted to the flow of heterogeneous, incompressible, inviscid, perfect conducting liquids between two rotating or nonrotating coaxial cylinders is divided into three parts. In the first part the stability of the liquid in question between two coaxial nonrotating cylinders with an applied magnetic field perpendicular to the flow is investigated. A sufficient condition for stability is found and if the motion is unstable an upper bound for the amplification factor is given. As a particular case the stability of the liquid with uniform steady velocity, and density varying as a function of a distance from the axis of the cylinders is discussed and it is found that the effect of the magnetic field makes the flow more stable.