Pseudospin Models of Superconductors with Very Short Coherence Length

We discuss a few models developed for description of superconductivity with very short coherence length and point out their formal equivalence to specific spin models, such as an anisotropic Heisenberg model (s = 1/2) with two- and four-spin exchange coupling and with fixed magnetization in the z-direction, an XY-Z model with single ion anisotropy and a Kondo-lattice model with anisotropic on-site exchange. New results concerning the phase diagram of the Hubbard model with strong attraction, the electromagnetic properties of systems with the first order superconducting transition and a possibility of local charge moment compensation in systems of coexisting bound pairs and itinerant electrons are presented.