The principal goal of astrobiology is the search for extraterrestrial life forms. A key aspect is the study of the ability of different kinds of terrestrial organisms to support simulated extraterrestrial environmental conditions. Mosses are multicellular green plants, poorly studied from an astrobiological perspective. In this paper, we report experimental results obtained using two species of moss, which demonstrate that both the spores of the moss Funaria hygrometrica as well as the desiccated vegetative gametophyte shoots of the moss Tortella squarrosa (Pleurochaete squarrosa) were capable of resisting Simulated Martian Environmental Conditions (SMEC): Mars simulated atmospheric composition 99.9% CO2, and 0.6% H2O with a pressure of 7 mbars, -73 oC and UV irradiation of 30 mW cm-2 in a wavelength range of 200-400 nm under a limited short time of exposition of 2 hours. After being exposed to SMEC and then transferred to an appropriate growth medium, the F. hygrometrica spores germinated, producing typical gametophyte protonemal cells and leafy shoots. Likewise, detached leaves from SMEC-exposed gametophyte shoots of T. squarrosa retained the ability to produce new protonemata and shoots under suitable growth conditions. Furthermore, we studied the tolerance of these moss structures to a thermal stress of 100 °C for 1 h; in both cases the spores and shoots were capable of resisting this heat treatment. Our study using FT-Raman and FT-IR vibrational spectroscopy demonstrated that neither spores nor shoots apparently suffered significant damage in their biomolecular makeup after being subject to these stress treatments. The implications of these findings for the search of life on Mars are discussed.