The deactivation of a composite catalyst based on HZSM-5 zeolite (agglomerated in a matrix using boehmite as a binder) has been studied during the transformation of dimethyl ether into light olefins. The location of the trapped/retained species (on the zeolite or on the matrix) has been analyzed by comparing the properties of the fresh and deactivated catalyst after runs at different temperatures, while the nature of those species has been studied using different spectroscopic and thermogravimetric techniques. The reaction occurs on the strongest acid sites of the zeolite micropores through olefins and alkyl-benzenes as intermediates. These species also condensate into bulkier structures (polyaromatics named as coke), particularly at higher temperatures and within the meso- and macropores of the matrix. The critical roles of the matrix and water in the reaction medium have been proved: both attenuating the effect of coke deposition.