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Constraints on the general 2HDM ("Model II") are obtained from the existing$(g-2)_{\mu}$ data including limits on Higgs bosons masses from LEP I data. Weconsider separately two cases: with a light scalar $h$ and with a lightpseudoscalar $A$, assuming ${M_{h}+M_{A}} \ge {M_{Z}}$. The charged Higgscontribution is also included. It is found that already the present$(g-2)_{\mu}$ data improve limits obtained recently by ALEPH collaboration on$\tb$ for the mass of the pseudoscalar below $ \mr$ 2 GeV. The improvement inthe accuracy by factor 20 in the forthcoming E821 experiment may lead to morestringent, than provided by ALEPH group, limits up to $M_A\sim$ 30 GeV if themass difference between $h$ and $A$ is $\sim M_Z$. Similar results should holdfor a light scalar scenario as well.Comment: 19 pages, including 5 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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Constraining the two Higgs doublet model by present and future(g−2)μdata