For decades, it was thought that prokaryotes did not have circadian clocks. Then, a clock was discovered in a unicellular cyanobacterium, Synechococcus (later also in Synechocystis  and Trichodesmium ) which quickly became an important model in the study of circadian rhythms in general. Still, it was thought, for ten years or so, that no other prokaryotes had a circadian clock. Recently, the clock genes were found in filamentous (chain-forming) cyanobacteria, as well as a whole host of other bacteria and archaea. However, having clock genes does not neccessarily translate into having a functioning clock - the genes may have other functions (e.g., photoreception, or DNA repair) in bacteria other than Synechococcus.
So, two recent papers tried to address this question - do photosynthetic bacteria exhibit circadian rhythms? And the results of the two studies, in two different species of bacteria, have some interesting similarities to each other, so let's look at them in parallel.
Van Praag et al., used Rhodospirillum rubrum, a gram-negative purple non-sulfur bacteria. Min et al., also chose a purple photosynthetic bacterium Rhodobacter sphaeroides. In the former, the measured output was hydrogenase uptake, while in the latter a battery of luciferase reporter genes was inserted in the genome - strains exhibiting fluoresecence (presumably those in which the construct got inserted behind a promoter) were used in the study.
In the first study, hydrogenase uptake was measured in unoxic (anaerobic) conditions in constant light (LL) at 32oC, and in constant darkness at 32oC and 16oC. In each of the three conditions, a rhythm was observed. The period of the freerunning rhythms was markedly different between the three conditions. In LL-32oC, period was ultradian: 12.1 hours. In DD at 32oC, the period was also ultradian: 14.8 hours. Only in DD at 16oC was the rhythm within a circadian range: 23.4 hours.
In the second study, light output was measured in three experiments. In all three, bacteria were assayed in constant darkness at 23oC. In the first and second groups, bacteria were pre-treated and their putative clocks entrained by a warm-cold-warm cycle prior to release into constant conditions. In the third group, the pre-treatments was exposure to a light-dark cycle prior to release into constant conditions. The first group was tested under aerobic conditions, while the second and the thir group were tested under anaerobic conditions.
Again, rhythms were observed in all three groups. What was observed was a difference in phase at which the rhythm begins dependent on the type of entraining cycle preceding the testing. The most important difference, however, was the difference in the freerunning period between the aerobic and anaerobic treatments. In the aerobic group, period was circadian: 20.5 hours. In the anaerobic conditions, the period was ultradian: 10.6 and 12.7 in groups II and III respectively.
What does this all mean? Temperature, light and oxygenation all appeared to have an effect on period. These experiments are difficult to do - if one was working with rodents or insects, the natural thing would be to test a large number of animals at several different temperatures to test for the possible lack of temperature compensation of the circadian rhythm, as well as at several different light intensities to test for the Aschoff's Rule. It is possible that this is a circadian clock that is not well temperature compensated, that is extremely sensitive to light, and that is based on the red-ox environment.
The way the studies have been reported, it is not clear that the rhythms are actually circadian, or if it just happened that some of the rhythms fell into the circadian range by accident. What is clear is that these bacteria generate endogenous rhythms. Are these rhythms circadian or not, and if so, are they driven by core-clock genes kaiA, kaiB and kaiC remains to be elucidated in the future.
 Aoki S, Kondo T, Wada H, and Ishiura M (1997) Circadian rhythm of the cyanobacterium Synechocystis sp. strain PCC 6803 in the dark. J Bacteriology 179:5751-5755.
 Chen YB, Domonic B, Mellon MT, and Zehr JP (1998) Circadian rhythm of nitrogenase gene expression in the diazotrophic filamentous nonheterocystous cyanobacterium Trichodesmium sp. strain IMS 101. J Bacteriology 180:3598-3605.
 Esther Van Praag, Robert Degli Agosti and Reinhard Bachofen, Rhythmic Activity of Uptake Hydrogenase in the Prokaryote Rhodospirillum rubrum, JOURNAL OF BIOLOGICAL RHYTHMS, Vol. 15 No. 3, June 2000 218-224
 Hongtao Min, Haitao Guo, Jin Xiong, Rhythmic gene expression in a purple photosynthetic bacterium, Rhodobacter sphaeroides, FEBS Letters 579 (2005) 808-812