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We study Gowdy spacetimes in the Einstein-Maxwell-dilaton-axion system and show by the Fuchsian algorithm that they have in general asymptotically velocity-term dominated singularities. The families of the corresponding solutions depend on the maximum number of arbitrary functions. Although coupling of the dilaton field with the Maxwell and/or the axion fields corresponds to the ``potential’’ which appears in the Hamiltonian of vacuum Bianchi IX spacetimes, our result means that the spacetimes do not become Mixmaster necessarily.

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