The aim of circular order aggregation is to find a circular order on a set of n items using angular values from p heterogeneous data sets. This problem is new in the literature and has been motivated by the biological question of finding the order among the peak expression of a group of cell cycle genes. In this paper, two very different approaches to solve the problem that use pairwise and triplewise information are proposed. Both approaches are analyzed and compared using theoretical developments and numerical studies, and applied to the cell cycle data that motivated the problem.