  A generalization of the chiral effective lagrangian of order $p^2$ is
proposed which involves the $\eta'$-meson, its excitation, and the pseudoscalar
(PS) glueball. Model-independent constraints are found for the contributions to
the lagrangian of the above singlet states. Those allow one to independently
identify the nature of these singlet states in the framework of the approach.
The mixing among the iso-singlet states (including $\eta^8$-state) is analysed,
and the hierarchy of the mixing angles is described which is defined by the
chiral and large-$N_c$ expansions. The recent PCAC results are reproduced,
which are related to the problem of the renormalization-group invariant
description of the $\eta'$ and the PS glueball, and a further analysis of this
problem is performed.
