The paper presents an analysis of brachystochronous movement of a conservative system during the action of holonomous relations. More precisely, it deals with solving the assignment of moving a system on a configurational manifold from one given position, where it remains at rest, to another given position, for the shortest possible time. The differential equations of this movement are formulated, and several special cases are analyzed. The geometrical characteristics of the regions of the possible brachystochronous movements are also indicated.