  After the discovery of the Higgs boson in 2012 at the CERN Large Hadron
Collider (LHC), the study of its properties still leaves room for an extended
Higgs sector with more than one Higgs boson. 2-Higgs Doublet Models (2HDMs) are
well-motivated extensions of the Standard Model (SM) with five physical Higgs
bosons: two CP-even states $h$ and $H$, one CP-odd state $A$, and two charged
states $H^\pm_{}$. In this letter, we present the calculation of the full
next-to-leading order (NLO) QCD corrections to $hH$ and $AA$ production at the
LHC in the 2HDM at small values of the ratio of the vacuum expectation values,
$\tan\beta$, including the exact top-mass dependence everywhere in the
calculation. Using techniques applied in the NLO QCD SM Higgs pair production
calculation, we present results for the total cross section as well as for the
invariant Higgs-pair-mass distribution at the LHC. We also provide the
top-quark scale and scheme uncertainties which are found to be sizeable.
