Circadian clocks improve plant fitness in a rhythmic environment. As each cell has its own circadian clock, we hypothesized that sets of cells with different functions would have distinct rhythmic behaviour. To test this, we investigated whether different organs in field-grown sugarcane follow the same rhythms in transcription. We assayed the transcriptomes of three organs during a day: leaf, a source organ; internodes 1 and 2, sink organs focused on cell division and elongation; and internode 5, a sink organ focused on sucrose storage. The leaf had twice as many rhythmic transcripts (>68%) as internodes, and the rhythmic transcriptomes of the internodes were more like each other than to those of the leaves. Among the transcripts expressed in all organs, only 7.4% showed the same rhythmic pattern. Surprisingly, the central oscillators of these organs – the networks that generate circadian rhythms – had similar dynamics, albeit with different amplitudes. The differences in rhythmic transcriptomes probably arise from amplitude differences in tissue-specific circadian clocks and different sensitivities to environmental cues, highlighted by the sampling under field conditions. The vast differences suggest that we must study tissue-specific circadian clocks in order to understand how the circadian clock increases the fitness of the whole plant.