  We investigate the production of Higgs bosons $A/h$ via the Yukawa process
$Z\ra f\bar{f} \ra f\bar{f} A/h $ taking into account QCD corrections and
fermion mass effects. We estimate the discovery reach of this process and/or
bounds on the parameter space of two-Higgs doublet models which can be derived
from the analysis of $b {\bar b} \tau^+ \tau^-$ events at LEP1. These limits
have important consequences for extended models of electroweak interactions and
their experimental verification/improvement are welcome.
