Endocycles are variant cell cycles comprised of DNA Synthesis (S)- and Gap (G)-phases but lacking mitosis. Such cycles facilitate post-mitotic growth in many animal and plant cells – in fact endocycling is so ubiquitous that it probably accounts for nearly half the biomass on earth. DNA replication in endocycling Drosophila cells is triggered by Cyclin Dependent Kinase (CDK) activity, but this must be inactivated during each G-phase to allow pre-Replication Complex (preRC) assembly for the next S-phase. Using genetic tests in parallel with computational modeling, we discovered that Drosophila's endocycles are driven by a molecular oscillator in which the E2F1 transcription factor promotes Cyclin E expression and S-phase initiation, S-phase then activates the CRL4Cdt2 ubiquitin ligase, and this in turn mediates E2F1 destruction. Genetic tests performed in vivo as well as computational simulations indicated that, in this mechanism, rates of E2F1 accumulation can control the frequency of endocycle S phases and the final ploidy and size of cells. Hence understanding how E2F1 protein expression is affected by cell growth and growth factor signaling is key to understanding the control of cell cycle progression in these cells. Following this lead, we found that altering cell growth by changing nutrition or TOR signaling impacts E2F1 translation, and that this connection makes endocycle progression growth-dependent. Finally, assays in cultured cells showed that the 5' UTR of E2F1 mRNA is important in mediating its translational control, likely in response to TOR and other growth-regulatory signals. Many of the regulatory interactions essential to the growth- and translation-dependent G1/S cell cycle oscillator we describe are conserved, suggesting that elements of this mechanism may act in most growth-dependent cell cycles in animal and plant cells. Future studies will combine genetic and computational analyses to explore how this mechanism functions in proliferating insect and human cells.