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Magne de la Croix (1936) from Argentina was the first to study evolution of tetrapod gaits. Also, the oldest trackways of mammaloid galloping, known as Ameghinichnus Casamiquela, 1964, were first found in Argentina. This Jurassic ichnogenus was initially ascribed to pantotherians and then to multituberculates or even tritylodonts or trithelodonts. However, its gait was not analyzed properly until now. Our analysis is based on the cast of the holotype MLP-60-X-31-14 exposed in the Ameghino’s home museum in Lujan. The gait is the paired gallop (bound) with 100 mm stride length. For the similar-sized laboratory mouse the stride/speed equation is known. So, it can be calculated that Ameghinichnus galloping speed was about 0.75 m/s. Extant mammals don't gallop so slowly: in the laboratory mouse the trot-gallop transition occurs at 1.1 m/s and in similar-sized wild rodents it takes place at even higher speeds. The sluggishness of Ameghinichnus may have been due to steeper trajectory of jumps than in any modern bounding mammal. In spite of steep jumps, Ameghinichnus obviously surpassed anurans in the ability to sustain horizontal speed from jump to jump, as seen from the fact that it landed the hindlimbs in front of the forelimbs. It may have even produced a brief jump (known as the cross-limbed aerial phase) by the forelimb thrust. Similar to mice, its hindlimb was digitigrade and forelimb was plantigrade. In addition, its manus was specifically in-fingered, which feature in anurans helps to prevent hitting the chin after jump. This precaution would be superfluous with the parasagittal forelimbs, so we conclude that in Ameghinichnus the forepaw in-fingerness was associated with sprawling stance. The in-fingered forelimbs were acquired by various tetrapods well before the origin of jumping gaits. Their use can be shown on the Late Permian pareiasaurian trackways from the Severnaya Dvina river basin in Russia. The longest trackway is 16.5 m long, 80 cm wide and includes 15 full strides. Footprints are deep, which means that the ground was soft and that the body weight was not supported by water. Pareiasaurians are short-bodied quadrupeds: available data suggest that their glenoacetabular length could be hardly more than 6 times greater than the pes length. Given this ratio, the gait of the trackway must have been the slow pace, where four-legged phases alternate with ipsilateral two-legged ones. With the barrelshaped body and sprawling limbs, the animal could only pace tilting from side to side in a manner of the “walking rocking bullcalf” (Russian traditional wooden toy). Tilting of the body must have been produced by means of a medially-directed push of the ipsilateral limb pair which was to be lifted off the ground in the next phase. The footprints show the signs of such push: first, there are definite imprints of the inward-pointing claws of the forepaws; second, the floor in the hindprints is gently but persistently lowering mediad. Generally, pace is considered impossible for sprawling quadrupeds. This constraint for the stepping sequence is aimed to sustain sprawler’s static equilibrium. However, the constraint is entirely disabled on sticky substrata. On swamps, which must have been the commonplace for pareiasaurians as well as stegocephalians, unsticking of any limb inevitably causes loss of balance and requires tilting of the body to the opposite side. In this case, rocking from side to side in slow pace may be of advantage. Noteworthy, the extant spiny anteater Zaglossus, in spite of the sprawling limb posture, uses a special kind of walk with the phases of ipsilateral pace-like support. According to our videorecords, rocking movements are driven in Zaglossus by its peculiar in-fingered forelimbs bearing strong claws. We hypothesize, that the therian gallop evolved from the pace-like gait of Paleozoic infingered barrel-bodied swamp-walkers, bypassing the trot-like gaits typical to modern lizards, which were hitherto regarded as inevitable. Roughly speaking, the process can be modeled by an imaginary pareiasaurian-Zaglossus-Ameghinichnus sequence. The forepaw in-fingerness was apparently lost together with acquisition of parasagittal stance for gallop perfection.