This study aims to investigate some characteristics of the moist processes of the Madden-Julian oscillation (MJO), by making use of joint HDO (or δD) and H2O vapor measurements. The MJO is the main intraseasonal mode of the tropical climate but is hard to properly simulate in global atmospheric models. The joint use of δD-H2O diagnostics yields additional information compared to sole humidity measurements. We use midtropospheric Infrared Atmospheric Sounding Interferometer (IASI) satellite δD and H2O measurements to determine the mean MJO humidity and δD evolution. Moreover, by making use of high temporal resolution data, we determine the variability in this evolution during about eight MJO events from 2010 to 2012 (including those monitored during the DYNAMO (the Dynamics of the MJO), CINDY (Cooperative Indian Ocean Experiment in Y2011) campaign). These data have a higher spatiotemporal coverage than previous δD measurements, enabling the sampling of individual MJO events. IASI measurements over the Indian Ocean confirm earlier findings that the moistening before the precipitation peak of an MJO event is due to water vapor slightly enriched in HDO. There is then a HDO depletion around the precipitation peak that also corresponds to the moister environment. Most interevent variability determined in the current study occurs 5 to 10 days after the MJO event. In 75% of the events, humidity decreases while the atmosphere remains depleted. In a quarter of the events, humidity increases simultaneously with an increase in δD. After this, the advection of relatively dry and enriched air brings back the state to the mean. Over the maritime continent, δD-H2O cycles are more variable on time scales shorter than the MJO and the interevent variability is larger than over the Indian Ocean. The sequence of moistening and drying processes as revealed by the q-δD cycles can be used as a benchmark to evaluate the representation of moist processes in models. This is done here by comparing observations to simulations of the isotope enabled LMDZ (Laboratoire de Météorologie Dynamique Zoom) global climate model nudged with reanalysis wind fields. These simulations also give information to investigate possible physical origins of the observed q-δD cycles.