  The scenario of two mass-degenerate Higgs bosons within the general
two-Higgs-doublet model (2HDM) is revisited. We focus on the global picture
when two $CP$-even Higgs bosons of $h$ and $H$ are nearly mass-degenerate. A
global fit to the signal strength of the 125 GeV Higgs measured at the LHC is
performed. Based on the best-fit result of the 2HDM mixing angles
$(\alpha,\beta)$, theoretical constraints, charged and $CP$-odd Higgs boson
direct search constraints and the electroweak precision constraints are imposed
to the 2HDM parameter space. We present the signal predictions of the $(4b\,,
2b\,2\gamma)$ channels for the benchmark models at the LHC 14 TeV runs. We also
study the direct Higgs boson pair productions at the LHC, and the Z-associated
Higgs boson pair production search at the ILC 500 GeV runs, as well as the
indirect probes at the CEPC 250 GeV run. We find that the mass-degenerate Higgs
boson scenario in the Type-II 2HDM can be fully probed by these future
experimental searches.
