The apical region of the Drosophila testis contains a niche with two stem cell populations: germline stem cells (GSCs) and cyst progenitor cells (CPCs). Asymmetrical division of these stem cells leads to gonioblast daughters (which undergo further mitoses) and cyst cell daughters (which withdraw from the cell cycle and become quiescent). Although a considerable body of evidence indicates important roles for centrosomes in spindle orientation and asymmetrical division of GSCs, the behaviour and function of the centrioles in CPCs and their daughters remain unknown. Here, we show that quiescent cyst cells lose centrosome components after two divisions of the spermatogonia they envelop, but keep the centriolar component SAS-6. Cyst cells do have centriole pairs, but they are formed by a mother and a very short daughter that does not elongate or mature. The presence of procentrioles in quiescent cyst cells suggests that the centriole duplication cycle is uncoupled from the G1-S transition and that it might begin even earlier, in mitosis. Failure to enter the cell cycle might result in the improper recruitment of centriolar components at the mother centriole, thus hampering the full elongation of its daughter. Procentriole maturation defects could thus lead to the inability to maintain centrosomal components during development.