A link chain for use in the continuously variable transmission of the power train in a motor vehicle is assembled of pairs of composite identical or dissimilar links each having a stack of apertured plates, and of coupling units employing pairs of non-circular pins extending through registering portions of apertures in the respective stacks of plates. The pins are designed to cooperate with the plates to limit the extend of inward and outward pivotability of links of the respective pairs from positions of alignment, and the pins carry stops which act alone or cooperate with diaphragm springs or with other types of springs to prevent wobbling of the plates. The plates can be provided with projections which cooperate with the pins to limit the extent of pivotability of the pairs of links relative to each other and/or to prevent jamming of pairs of links in angular positions from which they cannot return to the positions of alignment. Each plate is traversed by two pairs of pins.