Models for the control of global cell-cycle transcription have advanced from a CDK-APC/C oscillator, a transcription factor (TF) network, to coupled CDK-APC/C and TF networks. Nonetheless, current models were challenged by a recent study that concluded that the cell-cycle transcriptional program is primarily controlled by a CDK-APC/C oscillator in budding yeast. Here we report an analysis of the transcriptome dynamics in cyclin mutant cells that were not queried in the previous study. We find that B-cyclin oscillation is not essential for control of phase-specific transcription. Using a mathematical model, we demonstrate that the function of network TFs can be retained in the face of significant reductions in transcript levels. Finally, we show that cells arrested at mitotic exit with non-oscillating levels of B-cyclins continue to cycle transcriptionally. Taken together, these findings support a critical role of a TF network and a requirement for CDK activities that need not be periodic.