Several evidences suggest that early Mars offered favorable conditions for long-term sustaining water. As a consequence, we can assume that in those days, endogenous chemical processes, or even primitive life, may have produced organic matter on Mars. Moreover, exogenous delivery from small bodies or dust particles is likely to brought fresh organic molecules to the surface of Mars until now. Organic matter is therefore expected to be present at the surface/subsurface of the planet. The search for these organic relics is one of the main objectives of Mars exploration missions. But current environmental conditions at the surface - UV radiation, oxidants and energetic particles - can generate physico-chemical processes that may affect organic molecules. Here we present results of laboratory investigations dedicated to monitor qualitative and quantitative evolutions of several organic molecules under simulated Martian surface ultraviolet light, mean temperature and pressure, using the Mars Organic Molecules Irradiation and Evolution setup. For each organic molecule, the nature of the evolution products (solid or gaseous) and the kinetic parameters (extrapolated half-life at Mars, quantum yields) were determined experimentally. The results show that when exposed to UV radiation, specific organic molecules lead to the formation of solid residues, probably of macromolecular nature, which could reach long term stability. On the other hand, we emphasize the study of the evolution of molecules in presence of nontronite, a clay mineral detected at the surface of Mars, highlights a strong protective effect of the clay reducing dissociation rates for some molecules, whereas a possible catalytic effect is tentatively observed for one studied molecule. These results are essential to support the analyses performed in situ by the past, current and future exploration missions. Moreover, the experimentally determined kinetic parameters provide new inputs for numerical modeling of Mars' current reservoir of organic molecules.