Endocycles are variant cell cycles comprised of DNA synthesis (S)- and gap (G)-phases but lacking mitosis(1,2). Such cycles facilitate post-mitotic growth in many invertebrate and plant cells, and are so ubiquitous that they may account for up to half the world's biomass(3,4). DNA replication in endocycling Drosophila cells is triggered by cyclin E/cyclin dependent kinase 2 (CYCE/CDK2), but this kinase must be inactivated during each G-phase to allow the assembly of pre-Replication Complexes (preRCs) for the next S-phase(5,6). How CYCE/CDK2 is periodically silenced to allow re-replication has not been established. Here, using genetic tests in parallel with computational modelling, we show that the endocycles of Drosophila are driven by a molecular oscillator in which the E2F1 transcription factor promotes CycE expression and S-phase initiation, S-phase then activates the CRL4(CDT2) ubiquitin ligase, and this in turn mediates the destruction of E2F1 (ref. 7). We propose that it is the transient loss of E2F1 during S phases that creates the window of low Cdk activity required for preRC formation. In support of this model overexpressed E2F1 accelerated endocycling, whereas a stabilized variant of E2F1 blocked endocycling by de-regulating target genes, including CycE, as well as Cdk1 and mitotic cyclins. Moreover, we find that altering cell growth by changing nutrition or target of rapamycin (TOR) signalling impacts E2F1 translation, thereby making endocycle progression growth-dependent. Many of the regulatory interactions essential to this novel cell cycle oscillator are conserved in animals and plants(1,2,8), indicating that elements of this mechanism act in most growth-dependent cell cycles.