  Electromagnetic form factors of hyperons ($\Lambda$, $\Sigma$, $\Xi$) in the
timelike region, accessible in the reaction $e^+e^- \to \bar YY$, are studied.
The focus is on energies close to the reaction thresholds, where the properties
of these form factors are significantly influenced by the interaction in the
final $\bar YY$ system. This interaction is taken into account in the
calculation, utilizing $\bar YY$ potential models that have been constructed by
the J\"ulich group for the analysis of data from the reaction $\bar pp \to \bar
YY$ in the past. The enhancement of the effective form factor for energies
close to the threshold, seen in experiments of $e^+e^- \to \bar \Lambda
\Lambda$ and $e^+e^- \to \bar \Sigma^0\Lambda$, is reproduced. With regard to
the reactions $e^+e^- \to \bar \Sigma^- \Sigma^+, \ \bar\Sigma^0\Sigma^0, \
\bar\Sigma^+\Sigma^-$ a delicate interplay between the three channels is
observed in the results at low energies, caused by the $\bar\Sigma\Sigma$
interaction. Predictions for the electromagnetic form factors $G_M$ and $G_E$
in the timelike region are presented for the $\Lambda$, $\Sigma$, and $\Xi$
hyperons.
