A series of seven dedicated Lyman-α observations of exospheric atomic hydrogen in the martian corona were performed in March 2005 with the ultraviolet spectrometer SPICAM on board Mars Express. Two types of observations are analyzed, observations at high illumination (for a solar zenith angle SZA equal to 30°) and observations at low illumination (for a solar zenith angle equal to 90° (terminator), and near the south pole). The measured Lyman-α emission is interpreted as purely resonant scattering of solar photons. Because the Lyman-α emission is optically thick, we use a forward model to analyze this data. Below the exobase, the hydrogen density is described by a diffusive model and above the exobase, it follows Chamberlain's approach with...