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The monsoons are defined by a seasonal reversal of winds that brings more than 80% of annual precipitation to India and the Sahel, which are largely dependent on them. Predicting their evolution under the influence of man - the so-called anthropogenic response - is therefore of the utmost importance, all the more so as these two regions will be home to two billion people by 2100. However, the monsoon projections we are currently able to provide are accompanied by major uncertainties concerning the amplitude and sometimes the very sign of these changes. Using recent simulations carried out for the 6th report of the Intergovernmental Panel on Climate Change (IPCC), we seek to understand the origin of these uncertainties in climate models. The performance of these models in reproducing historical trends (1850-2014) is a factor of confidence in their ability to predict the future. However, these historical trends are also marked by uncertainties. Consequently, the first question we want to answer is: can we explain the uncertainty of the models in simulating the evolution of the Indian and Sahelian monsoons over the historical period? Model errors in relation to an observed climatology calculated over a reference period of at least thirty years are called biases, and we wish to test the hypothesis that they may partly explain the different responses of the models. We first consider the case of India, and following this hypothesis, we show that the climatological temperature biases of models in the equatorial Pacific Ocean modulate the way they simulate the historical response of the Indian monsoon. Indeed, we show that by modulating the historical response of the Pacific Ocean, climatological biases in the latter affect the Indian monsoon via mechanisms similar to those linking ENSO (El Niño - Southern Oscillation) and monsoon interannual variability. We then reproduce the same study for the Sahelian monsoon, where we show that climatological temperature biases in all the Tropics are strongly linked to the way models simulate its historical evolution. We do not, however, identify the precise physical mechanism linking this bias to the Sahelian monsoon, but we do show that the latter is strongly dependent on the way models simulate the response of the inter-hemispheric temperature gradient, which is physically consistent with the known role of this gradient as a modulator of the position of the inter-tropical convergence zone (ITCZ). In the second part of our investigations, we switch to projections (2014-2100) based on a pessimistic scenario of high emissions, and address the following question: what are the sources of uncertainty in the forced response of the monsoons within the projections? This time, we tackle the Sahel case first and link the diversity of responses across models to two factors: the response of the inter-hemispheric temperature gradient and that of the equatorial Pacific. The underlying mechanisms involve ITCZ migration and enhanced surface circulation for the first factor, and modulation of the Walker circulation and tropical waves for the second. These two factors account for 62% of the uncertainty in Sahel projections. Finally, we look at the future of the Indian monsoon, and show that its uncertainties are strongly linked to the temperature response of deserts from the Sahara to Pakistan, which also influences the response of the Sahelian monsoon. Indeed, the stronger the temperature response, the more pronounced the thermal depression over the deserts, the stronger the monsoon surface circulation and hence the precipitation.