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CH4 has been observed on Mars both by remote sensing and in situ during the past 15 yr. It could have been produced by early Mars serpentinization processes that could also explain the observed Martian remanent magnetic field. Assuming a cold early Mars, a cryosphere could trap such CH4 as clathrates in stable form at depth. The maximum storage capacity of such a clathrate cryosphere has been recently estimated to be 2 x 10(19) to 2 x 10(20) moles of methane. We estimate how large amounts of serpentinization-derived CH4 stored in the cryosphere have been released into the atmosphere during the Noachian and the early Hesperian. Due to rapid clathrate dissociation and photochemical conversion of CH4 to H-2, these episodes of massive CH4 release may have resulted in transient H-2-rich atmospheres, at typical levels of 10-20% in a background 1-2 bar CO2 atmosphere. The collision-induced heating effect of H-2 present in such an atmosphere has been shown to raise the surface temperature above the water freezing point. We show how local and rapid destabilization of the cryosphere can be induced by large events (such as the Hellas Basin or Tharsis bulge formation) and lead to such releases. Our results show that the early Mars cryosphere had a sufficient CH4 storage capacity to have maintained H-2-rich transient atmospheres during a total time period up to several million years or tens of million years, having potentially contributed to the formation of valley networks during the Noachian/early Hesperian.