The terrestrial origins of the diapsid Sauropterygia and Testudines are uncertain, with the latter being highly controversially discussed to this day. For only 15 Ma, Nothosauroidea lived in shallow-marine seas of the Triassic. Contrastingly, the pelagic Plesiosauria evolved in the Late Triassic, dispersed globally, and inhabited the oceans of the Jurassic and Cretaceous for approximately 135 Ma. Since the Cretaceous (~ 100 Ma), Chelonioidea, the modern sea turtles, have populated the oceans. All three groups evolved aquatic paraxial locomotion. Nothosaurs swam with their foreflippers, supported by the swimming tail. Plesiosaurs are the only tetrapods to have ever evolved four hydrofoil-like flippers. The plesiosaur flipper beat cycle has been debated for nearly two centuries. The different proposed locomotory styles (rowing, rowing-flight, underwater flight) are discussed in this review. A fourth gait that is employed by Carettochelys insculpta, which combines rowing and flying, is introduced. The osteology of the locomotory apparatus of nothosaurs and plesiosaurs is reviewed and compared to that of extant underwater-flying Chelonioidea. In conclusion, underwater flight remains the favoured locomotory style for plesiosaurs. Also, the review reveals that nothosaur locomotion has largely remained unstudied. Further, our understanding of joint morphologies and mobilities of the foreflipper in nothosaurs, plesiosaurs, and even recent sea turtles, and of the hindflipper in plesiosaurs, is very limited. It is crucial to the discussion of locomotion, to find out, if certain limb cycles were even possible, as evidence seems to point to the improbability of a rowing motion because of limited humerus and femur long axis rotation in plesiosaurs.

Diapsid Sauropterygia 和 Testudines 的陆地起源是不确定的，后者在今天被高度争议地讨论。仅 15 Ma，诺索龙科就生活在三叠纪的浅海中。相比之下，远洋蛇颈龙在晚三叠世演化，在全球范围内分散，并在侏罗纪和白垩纪的海洋中栖息了大约 135 Ma。自白垩纪（~ 100 Ma）以来，现代海龟 Chelonioidea 就在海洋中繁衍生息。所有三组都进化出了水生旁轴运动。诺托龙用它们的前鳍游泳，由游泳的尾巴支撑。蛇颈龙是唯一进化出四个类似水翼的鳍状肢的四足动物。蛇颈龙鳍状肢节拍周期已经争论了近两个世纪。建议的不同运动风格（划船、划船飞行、水下飞行）在这篇评论中进行了讨论。所采用的第四步态介绍了结合划船和飞行的Carettochelys insculpta。回顾了脊龙和蛇颈龙的运动器官的骨学，并将其与现存的水下飞行 Chelonioidea 的骨学进行了比较。总之，水下飞行仍然是蛇颈龙最喜欢的运动方式。此外，审查表明，诺索龙的运动在很大程度上仍未得到研究。此外，我们对蛇龙、蛇颈龙，甚至最近的海龟的前鳍和蛇颈龙的后鳍的关节形态和活动性的了解非常有限。对运动的讨论至关重要，找出某些肢体循环是否可能，因为证据似乎表明，由于蛇颈龙的肱骨和股骨长轴旋转受限，划船运动是不可能的。