The branching equilibria of a family of hydromagnetic equilibria are defined and studied. It is shown that if the laws of motion satisfy certain very general conditions, the results of this study permit the formulation of a criterion necessary for stability.A formalism independent of geometry is introduced and a variation principle is found from which the equilibrium equations are derived.The method proposed is used to study the stability of plane, cylindrical and rotational equilibria, and the results are compared with those obtained with explicit laws of motion.In cases of tubular configurations, a stricter criterion is obtained than that derived from classical magnetohydrodynamics since new possibilities of instability are taken into account corresponding to changes in topology of the magnetic surfaces.