A search for the rare decay $eta^{prime} to e^+e^-$ has been performed with the SND detector at the VEPP-2000 $e^+e^-$ collider. The inverse reaction $e^+e^- to eta^{prime}$ and $eta^{prime}$ five decay chains have been used for this search. The upper limit $Gamma_{eta^{prime} to e^+e^-}<0.002$ eV at the 90% confidence level has been set. A sensitivity of SND in a search for $eta to e^+e^-$ decay has been studied. For this perpose we have analyzed a data sample with an integrated luminosity of 108 nb$^{-1}$ collected in the center-of-mass energy range 520-580 MeV. There are no background events for the reaction $e^+e^- to eta$ with decay $eta to pi^0pi^0pi^0$ have been found. In the absence of background, a sensitivity to $B(eta to e^+e^-)$ of 10$^{-6}$ can be reached during two weeks of VEPP-2000 operation.
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