​The coelacanths (class Coelacanthi, superclass Sarcopterygii) are represented at the present day by only two species (genus Latimeria), but they have an extensive fossil record. The living fishes are characterized by the presence of a "rostral organ" in the snout that is part of the electrosensory system, and an intracranial joint or "hinge" in the skull that allows the anterior portion of the cranium to swing upwards, greatly enlarging the gape of the mouth (Smithsonian website ocean.si.edu/ocean-life/fish/coelacanth).

A large number of stem-group coelacanths have been identified. A recently published phylogenetic analysis is represented in the following phylogenetic time tree:
​Figure 1.    Time tree of the stem-Coelacanthi
​The oldest known stem-group Coelacanthi is Styloichthys changae found in the Early Devonian (Lochkovian) Xitun Formation at Qujing in East Yunnan, China (Zhu and Yu, 2002;Toriño et al, 2021). No image is available in the public domain, but  other stem-Coelacanthi for which public-domain images are available are shown below (click on image for a larger view):
​Figure 2. Images of  stem-group  coelacanths
The above images are placed in order from the most basal to those closest to the crown group, but no obvious trends can be seen except the establishment of a body form quite similar to that of modern coelacanths in most of the examples younger than the Middle Devonian. Apart from anomalies such as Allenypterus montanus, the gross body form has not changed much since that time. 

The crown-Coelacanthi are represented only by the two extant species of coelacanth, Latimeria chalumnae (the West Indian Ocean coelacanth; shown in the header above) and Latimeria menadoensis (the Indonesian coelacanth). No fossils are known from either species, so the crown group is entirely modern.
​
Given that no fossils are known from the crown-Coelacanthi and that the youngest known member of the stem group (Megalocoelacanthus) is at least 78 million years old, the time tree shown above (Figure 1) indicates that the stem-to-crown transition for the Coelacanthi lasted at least 326 million years. This is more than an order of magnitude longer than the duration of the corresponding transition for the Sarcopterygii.

References

Cavin, L., & Guinot, G. (2014). Coelacanths as “almost living fossils”. Frontiers in Ecology and Evolution, 2, 49.

Dutel, H., Maisey, J. G., Schwimmer, D. R., Janvier, P., Herbin, M., & Clément, G. (2012). The giant Cretaceous coelacanth (Actinistia, Sarcopterygii) Megalocoelacanthus dobiei Schwimmer, Stewart & Williams, 1994, and its bearing on Latimerioidei interrelationships. PLoS One, 7(11), e49911.

Dutel, H., Herbin, M., & Clément, G. (2015). First occurrence of a mawsoniid coelacanth in the Early Jurassic of Europe. Journal of Vertebrate Paleontology, 35(3), e929581.

Toriño, P., Soto, M., & Perea, D. (2021). A comprehensive phylogenetic analysis of coelacanth fishes (Sarcopterygii, Actinistia) with comments on the composition of the Mawsoniidae and Latimeriidae: Evaluating old and new methodological challenges and constraints. Historical Biology, 33(12), 3423-3443.

​Zhu, M., & Yu, X. (2002). A primitive fish close to the common ancestor of tetrapods and lungfish. Nature, 418(6899), 767-770.

Zhu, M., Yu, X., Lu, J., Qiao, T., Zhao, W., & Jia, L. (2012). Earliest known coelacanth skull extends the range of anatomically modern coelacanths to the Early Devonian. Nature Communications, 3(1), 1-8.
Image credits – stem-Coelacanthi
  • Header (Preserved specimen of Latimeria chalumnae in the Natural History Museum, Vienna, Austria): Alberto Fernandez Fernandez, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons
  • Figure 2 (Qingmenodus yui): Open Access article Lu, J., Zhu, M., Ahlberg, P. E., Qiao, T., Zhu, Y. A., Zhao, W., & Jia, L. (2016). A Devonian predatory fish provides insights into the early evolution of modern sarcopterygians. Science advances, 2(6), e1600154.
  • Figure 2 (Miguashaia spp.): DiBgd, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Diplocercides heiligostockiensis): Robert Gess, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Serenichthys kowiensis): Anton Brink, South African artist, Copyrighted free use, via Wikimedia Commons
  • Figure 2 (Allenypterus montanus, fossil): James St. John, CC BY 2.0 <https://creativecommons.org/licenses/by/2.0>, via Wikimedia Commons
  • Figure 2 (Allenypterus montanus, life restoration): Nobu Tamura, under Creative Commons Attribution- ShareAlike (CC BY-SA)  license
  • Figure 2 (Rebellatrix divaricerca): Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Hadronector donbairdi): Muséum de Toulouse Attribution-NoDerivs 2.0 Generic (CC BY-ND 2.0)
  • Figure 2 (Rhabdoderma exiguum): Earth Science Club of Northern Illinois (ESCONI), under Attribution-NonCommercial-NoDerivs 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Caridosuctor populosum): Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Piveteauia madagascariensis): Daderot, CC0, via Wikimedia Commons
  • Figure 2 (Laugia groenlandica): FunkMonk, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Coccoderma bavaricum): Géry PARENT, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Coelacanthus granulatus): Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Whiteia sp.): GhedoghedoGhedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Heptanema paradoxum): Giulio de Alessandri (died in 1921), Public domain, via Wikimedia Commons
  • Figure 2 (Luopingcoelacanthus eurylacrimalis, fossil): Open Access article Wen, W., Zhang, Q. Y., Hu, S. X., Benton, M. J., Zhou, C. Y., Tao, X., ... & Chen, Z. Q. (2013). Coelacanths from the Middle Triassic Luoping Biota, Yunnan, South China, with the earliest evidence of ovoviviparity. Acta Palaeontologica Polonica, 58(1), 175-193.
  • Figure 2 (Luopingcoelacanthus eurylacrimalis, life restoration): Open Access article Wen, W., Zhang, Q. Y., Hu, S. X., Benton, M. J., Zhou, C. Y., Tao, X., ... & Chen, Z. Q. (2013). Coelacanths from the Middle Triassic Luoping Biota, Yunnan, South China, with the earliest evidence of ovoviviparity. Acta Palaeontologica Polonica, 58(1), 175-193.
  • Figure2 (Yunnancoelacanthus acrotuberculatus): Open Access article Wen, W., Zhang, Q. Y., Hu, S. X., Benton, M. J., Zhou, C. Y., Tao, X., ... & Chen, Z. Q. (2013). Coelacanths from the Middle Triassic Luoping Biota, Yunnan, South China, with the earliest evidence of ovoviviparity. Acta Palaeontologica Polonica, 58(1), 175-193.
  • Figure 2 (Chinlea sorensoni): Nobu Tamura under a Creative Commons 3.0 Unported (CC BY-NC-ND 3.0) license
  • Figure 2 (Trachymetopon liasicum): Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Mawsonia gigas): DiBgd, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Axelrodichthys araripensis, fossil): Open Access article Cupello, C., Meunier, F. J., Herbin, M., Janvier, P., Clément, G., & Brito, P. M. (2017). The homology and function of the lung plates in extant and fossil coelacanths. Scientific Reports, 7(1), 1-8.
  • Figure 2 (Axelrodichthys araripensis, life restoration): judoliveira, under Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License
  • Figure 2 (Diplurus sp.): Tim Evanson, CC BY-SA 2.0 <https://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons
  • Figure 2 (Megalocoelacanthus dobiei): Gasmasque, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Libys superbus): Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Ticinepomis peyeri): Art by Nadine Bösch, photographed at Museum of Paleontology, Zurich by Ghedoghedo, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Foreyia maxkuhni, fossil): Tiia Monto, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Foreyia maxkuhni, life restoration): Alain Bénéteau, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons
  • Figure 2 (Holophagus sp.): Chillibilli, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Undina penicillate): Gunnar Creutz, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons
  • Figure 2 (Macropoma willemoesi): Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Macropoma mantelli): Gideon Algernon Mantell (1790-1852), Public domain, via Wikimedia Commons