Sala Seminari (Dip. Matematica).
In these models we deal with coupled pairs consisting of a map between manifolds and a spinorial field along this map. Originated from supersymmetric sigma models and supermanifold theory, they are recently analysed using the tools in nonlinear analysis. The Euler-Lagrangian system contains both a second order(Laplacian type) and a first order (Dirac type) elliptic equations. Some basic properties will be given as well as some example of the Dirac-harmonic maps.