The decay $J/psi rightarrow gamma gamma phi$ is studied using a sample of $1.31 times10^{9}$ $J/psi$ events collected with the BESIII detector. Two structures around 1475 MeV/c$^2$ and 1835 MeV/c$^2$ are observed in the $gamma phi$ invariant mass spectrum for the first time. With a fit on the $gamma phi$ invariant mass, which takes into account the interference between the two structures, and a simple analysis of the angular distribution, the structure around 1475 MeV/c$^2$ is found to favor an assignment as the $eta(1475)$ and the mass and width for the structure around 1835 MeV/c$^2$ are consistent with the $X(1835)$. The statistical significances of the two structures are $13.5 sigma$ and $6.3 sigma$, respectively. The results indicate that both $eta(1475)$ and $X(1835)$ contain a sizeable $sbar{s}$ component.
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