Later in the period Byzantine usage, the term tagma came to refer only to the standing troops, which were utilized for garrisoning in Constantinople  and in the surrounding areas. For the most part these units were an outgrowth of the former traced their origins to the Roman Imperial troops. By the 7th century, these had declined to little more than parade units, simply because of the revolts and uprisings within the powerful new districts, in particular the Opsician and Asian areas, which of all the themes were closest to the capitol. Within the first sixty years since its creation, Constantinople was involved in five revolts, culminating in the rebellion and usurpation of the throne by its Opsician commander . Emperor Constantine V (r. 741–775) in reviewing the problems with the old guard units, made significant changes and reformed them into new tagmata regiments. The main purpose of this change was to insure a set of loyal as well as professional soldiers , both as a defense against provincial revolts, and also, at the time, as a formation devoted to Constantine’s acceptance of the anti-religious image policies. These new tagmata were made up exclusively of heavy cavalry units  which were certainly more mobile than the theme troops, and were organized and maintained on a consistent basis. During the 8th and 9th centuries, their role was that of a central reserve, garrisoned in and around the capital, and in regions such as Trace and Bythnia  order to support the Empire’s determination in pursuing a defensive nature against her enemies. These new tagmata also were intended to form the core of any imperial army on campaign. These were then reinforced by the thematic troops (provincial levies), who were more concerned with local defense.
In addition, the tagmata, like the late Roman equivalent, they served very well as a recruiting and promotion ground for young officers for young men who had the opportunity to catch the attention of their seniors. A career in a tagma could lead to a major commands in the provincial thematic armies or court appointment. Officers in the tagmata were recruited basically from the relatively well-off urban and landed upper class and officialdom, of the Anatolian themes. These areas came more and more to control the higher military offices of the state.In spite of this, the tagmata, as indeed military and state service in general, offered a degree of mobility of a social type for the lower strata of society.
In the 9th and early 10th centuries, there were four tagmata proper (“τὰ δʹ τάγματα”):
• the Scholai (Gr. Σχολαί, “the Schools”), were the most senior unit, the direct successor of the imperial guards established by Constantine the Great (r. 306–337). The term scholarioi (σχολάριοι), was used as a general reference for all common soldiers of the tagmata.
• the Exkoubitoi or Exkoubitores (Lat. Excubiti, Gr. Ἐξκούβιτοι, “the Sentinels”), established by Leo 1.
• the Arithmos(Gr. Ἀριθμός, “Number”) or Vigla (Gr. Βίγλα, from the Latin word for “Watch”),meaning the ‘Guard Watch.” The regiment performed special duties on campaign, including guarding the imperial camp, relaying the Emperor’s orders, and guarding prisoners of war.
• the Hikanatol (Gr. Ἱκανάτοι, “the Able Ones”), established by Emperor Nikephoros I(r. 802–811) in 810. 
Other units closely related to the tagmata, and often included among them, were:
the Noumeroi (Gr. Νούμεροι, from the Latin numerus, (“number”) were a garrison unit for Constantinople. 
the Optimtoi (Gr. Ὀπτιμάτοι, from Latin optimates, “the best”), although formerly an elite fighting unit, had by the 8th century been reduced to a support unit, responsible for the mules of the army’s baggage train (the τοῦλδον, touldon).
the men of the central Imperial Fleet (βασιλικόν πλώιμον, basilikon plōimon), are also counted among the tagmata in some sources.
In addition, there was also the Hetaireia(Gr. Ἑταιρεία, “Companions”), which comprised the mercenary corps in Imperial service, subdivided in Greater, Middle and Lesser, each commanded by a respective Hetaireiarchēs.
The ongoing debate in considering the real size and the make-up of the imperial tagmata, because of the inaccuracy of the few sources of information (military manuals, lists of offices and Arab accounts, primarily from the 9th century) relating to them s still very much involved. The primary sources, which are the accounts of Arab geographers Ibn Khurdadhbah and Qudāmah are really not very precise, but they do provide the overall tagmata strength at 24,000. This figure has been seen by many scholars, as too high, and revised estimates put the strength of each tagma at 1,000–1,500 men. Others, accept these numbers, and correlate them with the lists of officers in the Kletorologion to reach an average size of 4,000 for each tagma (including the Optimatoi and the Noumeroi, for which it is explicitly stated that they numbered 4,000 each). 
The tagmatic units were all organized along similar lines. They were commanded by a domestikos except for the Vigla, which was commanded by a droungarios. He was assisted by one or two officers called topoteretes(Gr. τοποτηρητής, lit. “placeholder”, “lieutenant”), each of whom commanded one half of the unit. Unlike the thematic units, there were no permanent intermediate command levels (tourmarchai, chiliarchoi, or pentakosiarchai) until Leo VI introduced the droungarios ca. after 902. The largest subdivision of the tagmata was the bandon, commanded by a komēs (“count”), called skribōn in the Exkoubitores and tribounos (“tribune”) in the Noumeroi and Walls units. The banda in turn were divided in companies, headed by a kentarchos (“centurion”), or drakonarios (“draconarius”) for the Exkoubitores, and vikarios (“vicar”) for the Noumeroi and Walls units. The domestikos ton Scholon, the head of the Scholai regiment, became gradually more and more important, eventually coming to be the most senior officer of the entire army by the end of the 10th century.
The following table illustrates the structure of the Scholai in the 9th century, according to Treadgold:
In addition, there were a chartoularios (χαρτουλάριος, “secretary”) and a protomandator (πρωτομανδάτωρ, “head messenger”), as well as 40 standard bearers (βανδοφόροι, bandophoroi), of varying ranks and titles in each tagma, and 40 mandatores (“messengers”), for a total unit size of 4,125. On campaign, every tagmatic cavalryman was accompanied by a servant.
The following table illustrates the structure of the Scholai in the 9th century according to Threadgold: 
Officer (no.) Unit Subordinates Subdivisions
Domestikos (1) Tagma 4,000 20 banda
Topoteretes (1/2) 2,000 10 banda
Komes (20) Banda 200 5 kentarchiai
Kentarchos Kentarchia 40
The next table gives the evolution of the theoretical establishment size of the entire tagmatic force, again as calculated by Warren Threadgold:
Year Total Size
1. Kazhdan (1991), p. 2007;
2. Bury (1911), p. 47;
3. Threadgold (1995), p. 28;
4. Haldon (1999), p. 78;
5. Haldon (1984), pp. 228-235;
6. abcdef Bury (1911), p. 48;
7. Haldon (1999), pp. 270-271;
8. Haldon (1999), pp. 272-273;
9. Haldon (1999), p. 272;
10. Bury (1911), PP. 47-48;
11. Haldon (1999), p. 111;
12. Bury (1911), p. 60;
13. Bury (1911), p. 65;
14. Haldon (1999), p. 158;
15. Bury (1911), p. 66;
16. Bury (1911), p. 54;
17. Haldon (1999), p. 103;
18. Threadgold (1980), pp. 273-277;
19. Threadgold (1995), p. 102;
20. Threadgold (1995), p. 105;
21. Threadgold (1995), p. 78;
22. ab Threadgold (1995), p.103;
a: The main contemporary sources for the period from the 8th to the late 10th centuries are: i) the various lists of offices (Takita), including the Taktikon Uspensky (ca. 842), the Kletorologion of Philotheos (899), the various Byzantine military manuals, chiefly the Tactica of Leo VI the Wise; iii) the works of Arab geographers Ibn al-Fagih, Ibn Khurdadhbah and Qudamah ibn Ja’far, who preserve the earlier work of al-Jarmi that dates to ca. 840; and iv) the Administrando Imperio and De Ceremoniis of Emperor Constantine VII Porphyrogennetos.
• (French) H’ele’ne, Glykatzi-Ahrweiler (1960). “Recherches sur l’administration de l’empire byzantin aux IX-XIème siècles”. Bulletin de correspondance hellénique 84 (1): 1–111. doi:10,3406/bch, 1960, 1551
• Bury, John B.(1911). The Imperial Administrative System of the Ninth Century – With a Revised Text of the Kletorologion of Philotheos. Oxford University Publishing.
• McCotter, Stephen: Byzantine army, edited by Richard Holmes, published in The Oxford Companion to Military History. (Oxford University Press, 2001)
• Haldon, John F. (1995). “Strategies of Defence, Problems of Security: the Garrisons of Constantinople in the Middle Byzantine Period”. In Mango, Cyril; Dagron, Gilbert. Constantinople and its Hinterland: Papers from the Twenty-Seventh Spring Symposium of Byzantine Studies, Oxford, April 1993 (Ashgate Publishing).
• Treadgold, Warren T.: Notes on the Numbers and Organization of the Ninth-Century Byzantine Army, published in Greek, Roman and Byzantine Studies 21 (Oxford, 1980)
• Treadgold, Warren T.: The Struggle for Survival, edited by Cyril Mango, published in The Oxford History of Byzantium. (Oxford University Press, 2002).