  Using 15.1 pb^{-1} of data collected by CMD-2 in the phi-meson energy range,
the branching ratios of the following conversion decays have been measured:
B(\phi\to\eta e^+e^-) = (1.14\pm0.10\pm0.06)\cdot10^{-4}, B(\eta\to
e^+e^-\gamma) = (7.10\pm0.64\pm0.46)\cdot10^{-3}, B(\eta\to\pi^+\pi^-e^+e^-) =
(3.7^{+2.5}_{-1.8}\pm0.3)\cdot10^{-4}. The upper limits for the following rare
conversion decays have been obtained at the 90% confidence level:
B(\phi\to\eta\mu^+\mu^-) < 9.4\cdot10^{-6}, B(\eta\to e^+e^-e^+e^-) <
6.9\cdot10^{-5}.
