We consider the nonlinear eigenvalue problems u ″ + r f ( u ) = 0 , 0 < t < 1 , u ( 0 ) = 0 , u ( 1 ) = ∑ i = 1 m − 2 α i u ( η i ) , where m ≥ 3 , η i ∈ ( 0 , 1 ) , and α i > 0 for i = 1 , … , m − 2 , with ∑ i = 1 m − 2 α i < 1 ; r ∈ ℝ ; f ∈ C 1 ( ℝ , ℝ ) . There exist two constants s 2 < 0 < s 1 such that f ( s 1 ) = f ( s 2 ) = f ( 0 ) = 0 and f 0 : = lim u → 0 ( f ( u ) / u ) ∈ ( 0 , ∞ ) , f ∞ : = lim | u | → ∞ ( f ( u ) / u ) ∈ ( 0 , ∞ ) . Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.