We analyze the Two-Higgs-Doublet Models (2HDMs) of Type I and II for consistency with the latest measurements of the ~125.5 GeV Higgs-like signal at the LHC. To this end, we perform scans of the 2HDM parameter space taking into account all relevant pre-LHC constraints as well as the most recent limits coming from searches for heavy Higgs-like states at the LHC. The current status of the 2HDMs of Type I and II is discussed assuming that the observed 125.5 GeV state is one of the two CP-even Higgs bosons, either the lighter h or the heavier H. Implications for future experiments, including expectations regarding other lighter or heavier Higgs bosons are given. The possible importance of heavier Higgs bosons feeding the signals for the 125.5 GeV state is also evaluated.
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