The cortex of marine ooids and the agglutinating carbonate of grapestones are composed of identically shaped aragonitic particles, both rods and granules. In both cases, the particles are the product of a biomineralization by burrowing thallophytes, probably, blue?green algae. The key to formation of the ooid cortex is the process of grapestone aggregation. Burrowing algae bind together adjacent sedimentary grains, first by algal threads and mucilage, and then by endomucilage calcification. Later, the voids between component grains are filled by aragonitic rods embedded in algal mucus. Finally, this calcification can lead to an ooid cortex around the entire grapestone nucleus. While grapestone formation necessititates stability of the sediment, theformation of ob'ids requires sufficient grain movement to prevent the algae from binding adjacent grains. The conditions for Gold growth are: bright illumination of warm and shallow sea water supersaturated with respect to CaCO3. The secretion of aragonite by algae is interpreted as a possible physiological response to this particular environment. A genetic line is proposed which links ooids and grapestones with stromatolites and oncolites. On the other hand, aragonite secretion by thallophytes within the marine realm, may also contribute to a perhaps major extent to the formation of aragonitic mud. The biocalcification of primitive algae reveals to be one of the oldest and geologically most important processes for the formation of marine shallow water calcareous sediment. The response of the thallophytic algae to physicochemical differences of the environment can explain the facies differentiation into ooid sand, grapestone aggregate sand, and lime mud, respectively. Three conditions can exclude ooid or grapestone formation: 1. The skeletal grain on which burrowing algae settle yields more nutrients for the algae than the ambient water; 2. the calcareous or noncal? careous grains are deposited in sea water deeper than about 10 meters; 3. the grains are deposited in cold sea water, less saturated in respect to CaCO3 than normal to tropical and subtropical zones. The micritization of ooids (and probably also of other carbonate grains) is interpreted as an intra-granular cementation below a cover of algal mucilage. Structural differences between the cortex of a) marine ooids composed of rods and granules (i.e. of particles showing no crystalline faces and edges under the scanning electron microscope [= ?aphanohedral? habit of crystals]), and b) of other coated grains with a radial crystalline cortex (from hypersaline environments, caves or mines, or of synthetic origin etc.), are genetically significant and should be used in nomenclature of coated grains: It is suggested that only grains of type (a) are called ob'ids, while type (b) grains should be termed spheroids.