  We look at the prospects for detecting light bosons, $X$, at proposed Z
factories assuming a production of $10^{12}$ Z bosons. Such a large yield is
within the design goals of future FCC-ee and CEPC colliders. Specifically we
look at the cases where $X$ is either a singlet scalar which mixes with the
standard model Higgs or a vector boson with mass $1\lesssim M_X \lesssim 80$
GeV. We find that several channels are particularly promising for discovery
prospects. In particular $Z\rightarrow f \bar{f} X$ and $Z \rightarrow V_Q X$
gives a promising signal above a very clean standard model background. We also
discuss several channels that have too large a background to be useful.
