Individual neural progenitors generate different cell types in a reproducible order in the retina, cerebral cortex and probably in the spinal cord. It is unknown how neural progenitors change over time to generate different cell types. It has been proposed that progenitors undergo progressive restriction or transit through distinct competence states; however, the underlying molecular mechanisms remain unclear. Here we investigate neural progenitor competence and temporal identity using an in vivo genetic system--Drosophila neuroblasts--where the Hunchback transcription factor is necessary and sufficient to specify early-born cell types. We show that neuroblasts gradually lose competence to generate early-born fates in response to Hunchback, similar to progressive restriction models, and that competence to acquire early-born fates is present in mitotic precursors but is lost in post-mitotic neurons. These results match those observed in vertebrate systems, and establish Drosophila neuroblasts as a model system for the molecular genetic analysis of neural progenitor competence and plasticity.