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This study is aimed towards an advanced characterization of the material behavior of hot mix asphalt (HMA) under cyclic compressive loading. The triaxial cyclic compression test (TCCT), which today is mainly employed according to EN 12697-25 for the assessment of the resistance to permanent deformation, is thoroughly reviewed. The four main areas of research are (a) to introduce an alternative assessment method for the characterization of the resistance to permanent deformation, (b) to study the viscoelastic behavior in axial and radial direction and analyze the dynamic Poisson's Ratio and the dynamic shear modulus, (c) to develop an analytical model which predicts the viscoelastic material behavior of HMA from viscoelastic binder characteristics and volumetric characteristics of the mix and (d) to introduce an advanced TCCT with cyclic instead of static confining pressure which takes into account the viscoelastic material reaction of HMA and thus simulates the state of stress which occurs in a road pavement in a more realistic way.