Although circadian oscillators in diverse eukaryotes all depend on interlinked transcriptional feedback loops, specific components are not conserved across higher taxa. Moreover, the circadian network in the model plant Arabidopsis thaliana is notably more complex than those found in animals and fungi. Here, we combine mathematical modeling and experimental approaches to investigate the functions of two classes of Myb-like transcription factors that antagonistically regulate common target genes. Both CCA1/LHY- and RVE8-clade factors bind directly to the same cis-element, but the former proteins act primarily as repressors, while the latter act primarily as activators of gene expression. We find that simulation of either type of loss-of-function mutant recapitulates clock phenotypes previously reported in mutant plants, while simulated simultaneous loss of both type of factors largely rescues circadian phase at the expense of rhythmic amplitude. In accord with this prediction, we find that plants mutant for both activator- and repressor-type Mybs have near-normal circadian phase and period but reduced rhythmic amplitude. Although these mutants exhibit robust rhythms when grown at mild temperatures, they are largely arrhythmic at physiologically relevant but nonoptimal temperatures. LHY- and RVE8-type Mybs are found in separate clades across the land plant lineage and even in some unicellular green algae, suggesting that they both may have functioned in even the earliest arising plant circadian oscillators. Our data suggest that the complexity of the plant circadian network may have arisen to provide rhythmic robustness across the range of environmental extremes to which plants, as sessile organisms, are regularly subjected.