The Curiosity rover has analyzed various detrital sedimentary rocks at Gale Crater, among which fluvial and lacustrine rocks are predominant. Conglomerates correspond both to the coarsest sediments analyzed and the least modified by chemical alteration, enabling us to link their chemistry to that of source rocks on the Gale Crater rims. In this study, we report the results of six conglomerate targets analyzed by Alpha-Particle X-ray Spectrometer and 40 analyzed by ChemCam. The bulk chemistry derived by both instruments suggests two distinct end-members for the conglomerate compositions. The first group (Darwin type) is typical of conglomerates analyzed before sol 540; it has a felsic alkali-rich composition, with a Na₂O/K₂O > 5. The second group (Kimberley type) is typical of conglomerates analyzed between sols 540 and 670 in the vicinity of the Kimberley waypoint; it has an alkali-rich potassic composition with Na₂O/K₂O < 2. The variety of chemistry and igneous textures (when identifiable) of individual clasts suggest that each conglomerate type is a mixture of multiple source rocks. Conglomerate compositions are in agreement with most of the felsic alkali-rich float rock compositions analyzed in the hummocky plains. The average composition of conglomerates can be taken as a proxy of the average igneous crust composition at Gale Crater. Differences between the composition of conglomerates and that of finer-grained detrital sediments analyzed by the rover suggest modifications by diagenetic processes (especially for Mg enrichments in fine-grained rocks), physical sorting, and mixing with finer-grained material of different composition