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.
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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.
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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.