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Introduction: Until now it is not possible to determine the equation of state (EOS) of hadronic matter from QCD. One succesfully applied alternative way to describe the hadronic world at high densities and temperatures are effective models like the RMF-models [1], where the relevant degrees of freedom are baryons and mesons instead of quarks and gluons. Since approximate chiral symmetry is an essential feature of QCD, it should be a useful concept for building and restricting e ective models. It has been shown [2,3] that effective sigma-omega models including SU(2) chiral symmetry are able to obtain a reasonable description of nuclear matter and finite nuclei. Recently [4] we have shown that an extended SU(3) × SU(3) chiral sigma-omega model is able to describe nuclear matter ground state properties, vacuum properties and finite nuclei satisfactorily. This model includes the lowest SU(3) multiplets of the baryons (octet and decuplet[5]), the spin-0 and the spin-1 mesons as the relevant degrees of freedom. Here we will discuss the predictions of this model for dense, hot, and strange hadronic matter.