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We assume that the 125 GeV Higgs discovered at the LHC is the heavy CP-evenHiggs of the two-Higgs-doublet models, and examine the parameter space in theType-I, Type-II, Lepton-specific and Flipped models allowed by the latest Higgssignal data, the relevant experimental and theoretical constraints. Further, weshow the projected limits on $\tan\beta$, $\sin(\beta-\alpha)$, $Hf\bar{f}$ and$HVV$ couplings from the future measurements of the 125 GeV Higgs at the LHCand ILC, including the LHC with integrated luminosity of 300 fb$^{-1}$ (LHC-300fb$^{-1}$) and 3000 fb$^{-1}$ (LHC-3000 fb$^{-1}$) as well as the ILC at$\sqrt{s}=250$ GeV (ILC-250 GeV), $\sqrt{s}=500$ GeV (ILC-500 GeV) and$\sqrt{s}=1000$ GeV (ILC-1000 GeV). Assuming that the future Higgs signal datahave no deviation from the SM expectation, the LHC-300 fb$^{-1}$, LHC-3000fb$^{-1}$ and ILC-1000 GeV can exclude the wrong-sign Yukawa coupling regionsof the Type-II, Flipped and Lepton-specific models at the $2\sigma$ level,respectively. The future experiments at the LHC and ILC will constrain theHiggs couplings to be very close to SM values, especially for the $HVV$coupling.

Study of the heavy CP-even Higgs with mass 125 GeV in two-Higgs-doublet models at the LHC and ILC