Wherever the solar wind meets a neutral atmosphere, X-rays are emitted by charge-exchange processes between heavy solar wind ions and the neutrals. Using an empirical model of the proton flow near Mars we present computer simulations of X-ray emissions from this charge-exchange process in Mars' exosphere. We also discuss implications for remote sensing. Here we show that the total X-ray luminosity near Mars from charge-exchange is greater than 1025 eV/s for typical solar wind conditions. This flux is large enough to be detected by an X-ray satellite in Earth orbit. Thus, Mars belongs to a new class of X-ray objects in the sky, together with other non-magnetized planets, such as Venus. ¿ 2001 American Geophysical Union