Summary: The author considers a system of coupled nonlinear Sturm-Liouville boundary value problems
where , are real spectral parameters. It is shown that if the functions and are ‘generic’ then for all integers , there are smooth 2-dimensional manifolds , , of ‘semi-trivial’ solutions to the system which bifurcate from the eigenvalues , , of , , respectively. Furthermore, there are smooth curves , , along which secondary bifurcations take place, giving rise to smooth, 2-dimensional manifolds of ‘non-trivial’ solutions. It is shown that there is a single such manifold, , which ‘links’ the curves , . Nodal properties of solutions on and global properties of are discussed.