  The associated production of neutral Higgs bosons with the Z gauge boson is
investigated in the context of the future linear colliders, such as the ILC and
CLIC, within the general two-Higgs-doublet model (2HDM). We compute the
corresponding production cross-sections at one-loop, in full consistency with
the available theoretical and phenomenological constraints. We find that the
wave-function renormalization corrections to the external Higgs fields are the
dominant source of the quantum effects, which turn out to be large and
negative, and located predominantly in the region around \tan\beta=1 and
moderate values of the parameter \lambda_5 (being \lambda_5 < 0). This behavior
can be ultimately traced back to the enhancement potential of the triple Higgs
boson self-couplings, a trademark feature of the 2HDM with no counterpart in
the Higgs sector of the Minimal Supersymmetric Standard Model. The predicted
Higgs-strahlung rates comfortably reach a few tens of femtobarn, which means
barely 10^3 - 10^4 events per 500 inverse femtobarn of integrated luminosity.
Due to their great complementarity, we argue that the combined analysis of the
Higgs-strahlung events and the previously computed one-loop Higgs-pair
production processes could be instrumental to probe the structure of the Higgs
sector at future linac facilities.
