The FETI method is an iterative substructuring method using Lagrange multipliers. It is actively used in industrial--size parallel codes for solving difficult computational mechanics problems, for example the system ANSYS. Mortar finite elements are nonconforming finite elements that also allow for a geometrically nonconforming decomposition of the computational domain and for the optimal coupling of different variational approximations in different subdomains. We present a numerical study of three different FETI preconditioners for two dimensional, self-adjoint, elliptic equations discretized by mortar finite elements.