Abstract : We explore the possibilities in two-Higgs-doublet models (2HDMs) of Type I and Type II for Higgs states with mass below about 60 GeV, i.e. less than half of the ~125 GeV mass of the observed SM-like Higgs boson. We identify the latter as either the lighter or the heavier CP-even state, h or H, and employ scans of the 2HDM parameter space taking into account all relevant theoretical and experimental constraints, including the most up-to-date Higgs signal strength measurements. We find that, in both Type I and Type II models, such light Higgs states are phenomenologically viable and can lead to interesting signatures. Part of the relevant parameter space may be testable with the existing 8 TeV LHC data, e.g. by looking for direct production of the light state via gg-fusion or bb-associated-production using its \tau^+ \tau^- and \mu^+ \mu^- decays at low invariant mass.
