The aim of this paper is to study connected, unbounded sets of solutions of the non-cooperative elliptic system of equations with Neumann boundary conditions. The existence of such sets is obtained by proving the bifurcation from infinity. To this end we apply the degree for $G$-invariant strongly indefinite
"Connected sets of solutions for a nonlinear Neumann problem." Differential Integral Equations 30 (11/12) 833 - 852, November/December 2017.