Hydromagnetic structural and stability properties of global magnetic fields with current sheets are discussed in this paper. These fields describe solar coronal magnetic structures that form when a fresh magnetic field of opposite polarity has emerged into the corona containing a preexisting magnetic field. Three classes of axisymmetric fields are treated. The first is characterized by a continuous normal field distribution at the boundary and an infinitesimally thin current sheet in the field. As ideal hydromagnetic equilibria, these fields are globally stable, but they are resistively unstable within the current sheet. Magnetic reconnection is unavoidable no matter how large the electrical conductivity is. The other two classes of fields may be stable without this kind of resistive nonequilibrium. Of particular interest among them are equilibrium fields with finite-thickness current sheets in force balance with pressure gradients and gravity. These fields are shown to have enough free magnetic energy to let some parts of its field to become open during magnetic reconnection, an effect important for the dynamics of coronal mass ejections.