We study the pseudoscalar glueball and its first excited state by constructing three interaction Lagrangians. One produces the two- and three-body decays of the pseudoscalar glueball, JPC = 0−+, into (axial-)vector mesons, scalar glueball, and (pseudo)scalar mesons. The other two describe the two- and three-body decays of the first excited pseudoscalar glueball, JPC = 0∗−+, into (pseudo)scalar mesons, a scalar, and a pseudoscalar glueball. We compute the decay widths by fixing the mass of the ground state of a pseudoscalar glueball to 2.6 GeV and of its first excited state to 3.7 GeV, as predicted by lattice QCD in the quenched approximation. We present the results as branching ratios with a parameter-free prediction, which are interesting and relevant for the PANDA experiment at the upcoming FAIR facility experiment and running BESIII and Belle-II experiments. © 2024 Jagiellonian University. All rights reserved.