A fast method to incorporate the UV heating and the photochemistry of the neutral upper atmosphere of Mars into general circulation models (GCMs) is presented. On the basis of more detailed one-dimensional (1-D) models, the scheme we propose makes use of a division of the UV spectrum in 36 subintervals of 20 nm average width. Photoabsorption coefficients are computed allowing for overlapping and are tabulated as a function of suitable column abundances. The photochemistry proposed includes 12 compounds and uses the approximation of photochemical equilibrium for the three fastest species, OH, O(1D), and HO2. The behavior of the fast scheme is shown against detailed 1-D calculations. The resulting acceleration is about a factor 200 in the UV heating, while in the photochemistry it is about a factor 100 at 120 km and much larger below. The proposed scheme has already been implemented into the GCM developed at the Laboratoire de M¿t¿orologie Dynamique-CNRS in Paris (LMD), which therefore becomes the first single Martian GCM to cover the whole range of altitudes from the planet surface to the upper thermosphere. We present typical results of the Martian thermosphere obtained with the present scheme and the LMD-GCM, in order to illustrate its behavior and stability. In particular, we show the sensitivity of the Martian upper atmosphere's thermal structure to the local photochemistry. Comparisons with previous models are also presented, as first steps in an ongoing validation study, necessarily extensive for this kind of GCM, which will include more detailed comparisons with recent and future data from space missions.