We consider the nonlinear eigenvalue problems u″+λf(u)=0, 0<t<1, u(0)=0, u(1)=∑i=1m-2αiu(ηi), where m≥3, ηi∈(0,1), and αi>0 for i=1,…,m-2, with ∑i=1m-2αi<1, and f∈C1(ℝ\{0},ℝ)∩C(ℝ,ℝ) satisfies f(s)s>0 for s≠0, and f0=∞, where f0=lim|s|→0f(s)/s. We investigate the global structure of nodal solutions by using the Rabinowitz's global bifurcation theorem.