We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only parametrically definable subsets are finite unions of singletons and open intervals, and those where the definable subsets are finite union of singletons and c-convex subsets, where being c-convex is the analogue of being convex in the linearly ordered case.