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We calculate the decay widths of both the second and the third radialexcitations of $\eta$ and $\eta'$ within the framework of $^3P_0$ model. Aftercomparing the theoretical decay widths and decay patterns with the availableexperimental data of $\eta(1760)$, $X(1835)$, $X(2120)$ and $X(2370)$, we findthat the interpretation of $\eta(1760)$ and $X(1835)$ as the second radialexcitation of $\eta$ and $\eta'$ crucially depends on the measured mass andwidth of $\eta(1760)$, which is still controversial experimentally. We suggestthat there may be sizable $p\bar{p}$ content in $X(1835)$. $X(2120)$ and$X(2370)$ can not be understood as the third radial excitations of $\eta$ and$\eta'$, $X(2370)$ probably is a mixture of $\eta'(4{^1}{S}{_0})$ and glueball.

$X(1835)$ and the New Resonances $X(2120)$ and $X(2370)$ Observed by the BES Collaboration