The PROCESS (PRebiotic Organic ChEmistry on the Space Station) experiment was part of the EXPOSE-E payload outside the European Columbus module of the International Space Station from February 2008 to August 2009. During this interval, organic samples were exposed to space conditions to simulate their evolution in various astrophysical environments. The samples used represent organic species related to the evolution of organic matter on the small bodies of the Solar System (carbonaceous asteroids and comets), the photolysis of methane in the atmosphere of Titan, and the search for organic matter at the surface of Mars. This paper describes the hardware developed for this experiment as well as the results for the glycine solid-phase samples and the gas-phase samples that were used with regard to the atmosphere of Titan. Lessons learned from this experiment are also presented for future low-Earth orbit astrochemistry investigations.