In the present study we consider the theory of thermoelastodynamics in the case of materials with double porosity structure and microtemperature. This study is devoted to the investigation of a backward in time problem associated with double porous thermoelastic materials with microtemperature. In the first part of the paper, in case of the bounded domains the impossibility of time localization of solutions is obtained. This study is equivalent to the uniqueness of solutions for the backward in time problem. In the second part of the paper, a Phragmen-Lindelof alternative in the case of semi-infinite cylinders is obtained. keywordsThermoelasticity with double porosity Microtemperature Backward problem Impossibility of localization

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