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Many studies with atmospheric general circulation models (AGCMs) have demonstrated their usefulness in reconstructing past climates. In a new approach, we have used an AGCM to investigate the link between tracer cycles and climate. We consider in this paper the atmospheric cycle of windblown dust material from desertic areas and in part 2 the water isotope cycles. Studies from ice cores have shown a strong increase of the dust deposits during glacial periods, both over East Antarctica and Greenland. We do not know, however, whether this past increase is global or just a local feature, where the dust came from, and what are the mechanisms yielding this increase. We try to answer to these questions by using an AGCM including a model for the desert dust cycle to simulate the present-day and Last Glacial Maximum climates for February and August. The model simulates only a weak increase of the global atmospheric dust content. Stronger variations are obtained at a regional scale and are in good agreement with observations from deep-sea sediments. However, the model does not reproduce the great increase of die dust concentration in snow that has been observed in ice cores. Several model deficiencies can induce this model-data discrepancy as, for example, inaccuracies of the circulation patterns or of the dust model. However, most likely, the model fails to simulate the actual sources of dust.