A kinetic model has been proposed for the synthesis of dimethyl ether in a single reaction step from (H-2 + CO) and (H-2 + CO2), and the kinetic parameters have been calculated for a CuO-ZnO-Al2O3/gamma-Al2O3 bifunctional catalyst. The kinetic model suitably fits the experimental results obtained in an isothermal fixed bed reactor within a wide range of operating conditions: 225-325 degrees C; 10-40 bar; space time, 1.6-57.0 (g of catalyst) h (mol H-2)(-1). The crucial steps for modeling are the synthesis of methanol from (H-2 + CO) - synthesis from (H-2 + CO2) is not important-methanol dehydration (very fast), and the water-shift reaction (in equilibrium). The inhibiting effect of water is also taken into account in the synthesis of methanol and the formation of hydrocarbons. The advantage of carrying out methanol dehydration in situ is noteworthy, given that it allows for attaining yields higher than 60% of carbon converted into DME and 5% into methanol, when (H-2 + CO) is fed at 30 bar and 275 degrees C. At higher temperatures, hydrocarbons (mainly methane) are produced.