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

Quantum effects on Higgs-strahlung events at Linear Colliders within the general 2HDM