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In this paper are presented two extensions of the Rusinek&-Klepaczko constitutive relation [Rusinek A, Klepaczko JR. Shear testing of sheet steel at wide range of strain rates and a constitutive relation with strain-rate and temperature dependence of the flow stress. Int J Plasticity 2001;17:87&-115] to define the behaviour of aluminium alloys at wide ranges of strain rate and temperature. The formulationsreported extend the validity of the Rusinek&-Klepaczko model for the definition of particular aspects of the behaviour of aluminium alloys, namely the negative strain rate sensitivity and the viscous drag. Such formulations are applied to describe the thermo-viscoplastic behaviour of two commercial aluminium alloys (AA 5083-H116 and AA 7075) using experimental data available in the literature [Clausen AH, Børvik T, Hopperstad OS, Benallal A. Flow and fracture characteristics of aluminium alloy AA5083-H116 as function of strain rate, temperature and triaxiality. Mater Sci Eng A 2004;364:260&-72; El-Magd E, Abouridouane M. Characterization, modelling and simulation of deformation and fracture behaviour of the light-weight wrought alloys under high strain rate loading. Int J Impact Eng 2006;32:741&-58]. Their analytical results are compared with those obtained from the phenomenological constitutive relations reported in Clausen et al. (2004) and El-Magd and Abouridouane (2006). The best agreement with experiments is achieved by the predictions provided by the extended Rusinek&-Klepaczko models. Moreover, the formulations presented may be implemented into FE code using for example the algorithm reported in [Zaera R, Fernández-Sáez J. An implicit consistent algorithm for the integration of thermoviscoplasticconstitutive equations in adiabatic conditions and finite deformations.