Chain-rings set, for a power transmission system, which includes a chain, a first chain-ring, a second chain-ring where the first chain-ring is formed by a support part of the teeth and a teeth part, where the second chain-ring is formed by segments each formed by a support part of the teeth and a teeth part, which includes axial displacement means of the segments, where an up-shift segment of the segments has a first tooth which is the first which is engaged with the chain in the rotation movement, and where the displacement means are configured for moving the up-shift segment to an engaging position such that the first tooth can engage with an engaging link of the up-shift section of the chain, when the chain is engaged in the small chain-ring, and without the support part of the up-shift segment reaching the same plane than the support part of the first chain-ring, and to successively displace the other independent segments to an engaging position with the chain without the support parts of the independent segments reaching the same plane than the support part of the first chain-ring.