Abstract Inverse nodal problems for Sturm–Liouville equations associated with boundary conditions polynomially dependent on the spectral parameter are studied. The authors show that a twin-dense subset WB([a,b]) $W_{B}([a,b])$ can uniquely determine the operator up to a constant translation of eigenparameter and potential, where [a,b] $[a,b]$ is an arbitrary interval which contains the middle point of the domain of the operator and B is a subset of N $\mathbb {N}$ which satisfies some condition (see Theorem 4.2).