The preparation by physical coating of a bifunctional core-shell-structured catalyst (CZZr@S-11), using CuO-ZnO-ZrO2 (CZZr) as metallic function and SAPO-11 (S-11) as acid function, has been studied. The effects of calcination temperature and mass ratio between the metallic and acid functions (M/A) on their kinetic behavior for the synthesis of DME from syngas and CO2 feeds has been assessed. The reaction indices considered have been: the conversion of COx (CO + CO2) and CO2; yields and selectivities of dimethyl ether (DME), methanol and hydrocarbons; and stability. The experiments have been carried out in a fixed-bed reactor (275 degrees C, 30 bar). The CZZr@S-11 catalyst prepared under suitable conditions (calcination at 400 degrees C and M/A of 1/2), shows better reaction indices than the hybrid catalyst (CZZr/S-11), prepared by physical mixture of the individual functions, which is explained by the advantages of the core-shell structure, especially interesting for the valorization of CO2.