In a process for purifying a hydrogen stream, the stream is contacted with a first washing fluid in a first purification zone under conditions effective to transfer at least some water from the hydrogen stream to the first washing fluid, thereby transforming the hydrogen stream into a water-depleted hydrogen stream. At least a portion of the water-depleted hydrogen stream may then be transferred from the first purification zone to a second purification zone, where it is contacted with a second washing fluid under conditions effective to transfer at least some oxygenates from the water-depleted hydrogen stream to the second washing fluid.