Quasi-flat zones are based on the constrained connectivity paradigm and they have proved to be effective tools in the context of image simplification and super-pixel creation. When stacked, they form successive levels of the α-or ω-tree powerful representations. In this paper we elaborate on their extension to angular data, whose periodicity prevents the direct application of grayscale quasi-flat zone definitions. Specifically we study two approaches in this regard, respectively based on reference angles and angular distance computations. The proposed methods are tested both qualitatively and quantitatively on a variety of angular data, such as hue images, texture orientation fields and optical flow images. The results indicate that quasi-flat zones constitute an effective means of simplifying angular data, and support future work on angular tree-based representations .