We extend the two-Higgs doublet models of Type I and Type II by adding a real gauge-singlet scalar S dark matter candidate (2HDMS models). We impose theoretical constraints deriving from perturbativity, stability, unitarity and correct electroweak symmetry breaking and require that the lightest CP-even Higgs, h , fit the LHC data for the ∼ 125 . 5 GeV state at the 68% C.L. after including existing constraints from LEP and B physics and LHC limits on the heavier Higgs bosons. We find that these models are easily consistent with the LUX and SuperCDMS limits on dark-matter-Nucleon scattering and the observed Ω h 2 for S masses above about 55 GeV. At lower m S , the situation is more delicate. For points with m S in the 6-25 GeV range corresponding to the CDMS II and CRESST-II positive signal ranges, the dark-matter-Nucleon cross sections predicted by the Type I and Type II models more or less automatically fall within the 95%–99% C.L. signal region boundaries. Were it not for the LUX and SuperCDMS limits, which exclude all (almost all) such points in the case of Type I (Type II), this would be a success for the 2HDMS models. In fact, in the case of Type II there are a few points with 5 . 5 GeV ≲ mS ≲ 6 . 2 GeV that survive the LUX and SuperCDMS limits and fall within the CDMS II 99% C.L. signal region. Possibilities for dark matter to be isospin-violating in this 2HDMS context are also examined

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