Polymer-electro-conductive nanostructured composites have gained much interest, due to their potential use as flexible large size sensors with superior mechanical and electrical properties. We use TMA (thermo mechanical analysis) and DMA (dynamic mechanical analysis) to study the thermal expansion as well as the temperature and frequency dependence of the dynamic elastic susceptibility of various nanostructured composite materials. In this work we present a brief description of the method, the sample geometries used, etc. In the second part we present results of recent TMA and DMA measurements of polyisoprene/multiwall carbon nanotube (PMWCNT) composites (Fig.1) and Elastomer/MoS2 (2d) and Elastomer/Mo6S2I8 (nanowire) composites. For PMWCNT composites above the glass transition temperature Tg the composites with phr values above the electric percolation threshold [red (12 phr) and blue (16 phr) curves in Fig.1] show a ca. 30% higher thermal expansion coefficient than those with phr below the percolation threshold. Below Tg this difference disappears. This strong influence of filler concentration on thermal expansivity and its relation to the glass transition is discussed.