It is a simple unicellular plant. The individuals are spherical, ovoid subcylindrical or ellipsoidal. In many species a papilla like out growth is visible in the anterior region. The protoplast is surrounded by a definite layer of cellulose wall and motile cells of some species have a gelatinous pectic sheath outside the cellulose layer.
Most of the species have a single large cup shaped chloroplast and occupy most of protoplast.
But in other species the chloroplast may be reticulate, stellate or discoid. Chloroplast of most of species have a single pyrenoid but some of the species have two (C. debaryana) or several (C. gigantea). Some species like C. reticulata do not have pyrenoids.
At the pointed anterior end arise two flagella emerging through the same or seperate canals. The flagella are acronematic (whiplash) and of equal length. Each flagellum has a granule (blepharoplast) at the points of its origin. They are connected together by a transverse fibre called paradesmose, which is again connected to intranuclear centrosome of the nucleus. The flagella are organelle of locomotion.