Authors:de Wit et alAbstract:Three Earth-sized exoplanets were recently discovered close to the habitable zone of the nearby ultracool dwarf star TRAPPIST-1. The nature of these planets has yet to be determined, since their masses remain unmeasured and no observational constraint is available for the planetary population surrounding ultracool dwarfs, of which the TRAPPIST-1 planets are the first transiting example. Theoretical predictions span the entire atmospheric range from depleted to extended hydrogen-dominated atmospheres. Here, we report a space-based measurement of the combined transmission spectrum of the two inner planets made possible by a favorable alignment resulting in their simultaneous transits on 04 May 2016. The lack of features in the combined spectrum rules out cloud-free hydrogen-dominated atmospheres for each planet at 10-σ levels; TRAPPIST-1 b and c are hence unlikely to harbor an extended gas envelope as they lie in a region of parameter space where high-altitude cloud/haze formation is not expected to be significant for hydrogen-dominated atmospheres. Many denser atmospheres remain consistent with the featureless transmission spectrum---from a cloud-free water vapour atmosphere to a Venus-like atmosphere.