[en] We have performed neutron-capture gamma-ray studies on natural and enriched targets of ¹³⁴Ba in order to investigate the nuclear levels of ¹³⁵Ba. The low-energy level spectra were compared with the calculations using the interacting-boson-fermion model (IBFM) and the cluster-vibration model. The level densities up to 5 MeV that are calculated within the IBFM are in accordance with the constant temperature Fermi gas model. From the spin distribution we have determined the corresponding spin cutoff parameter σ and compared it to the prediction from nuclear systematics