A derailleur apparatus for bicycles, comprising: an installation housing, installed on a handle of a bicycle; and a gearshift control assembly, installed inside the installation housing, having a movable first lever for cable-pulling, a ratchet assembly having a sidewall surface to mount a ratchet plate, a movable second lever for cable-releasing and an index claw, the ratchet plate including a plurality of teeth, the first lever having a first pawl for meshing one tooth of the ratchet plate so that the ratchet assembly is kept at an initial position, the ratchet assembly rotating toward a first direction to perform an up-shift movement while the first lever is pulled to move in a cable-pulling direction so as to have the first pawl to mesh another tooth of the ratchet plate; characterized in that the index claw formed as a plate member includes a matching member and a second pawl for meshing one tooth of the ratchet plate, the index claw being connected to a return pin, the return pin driving back the index claw to its initial position, wherein one end of the second lever and the matching member form a first specific contact and keep a specific actuation relationship, and in that the direction, to which the second lever is able to be moved in order to release the cable, includes at least two different directions; whereby, while the second lever is determined to move in a direction so as to form a second specific contact with the matching member, the index claw rotates to have the second pawl to mesh with another tooth of the ratchet plate, such that a down-shift movement is performed by having the ratchet assembly to rotate toward a second direction. an installation housing, installed on a handle of a bicycle; and a gearshift control assembly, installed inside the installation housing, having a movable first lever for cable-pulling, a ratchet assembly having a sidewall surface to mount a ratchet plate, a movable second lever for cable-releasing and an index claw, the ratchet plate including a plurality of teeth, the first lever having a first pawl for meshing one tooth of the ratchet plate so that the ratchet assembly is kept at an initial position, the ratchet assembly rotating toward a first direction to perform an up-shift movement while the first lever is pulled to move in a cable-pulling direction so as to have the first pawl to mesh another tooth of the ratchet plate; characterized in that the index claw formed as a plate member includes a matching member and a second pawl for meshing one tooth of the ratchet plate, the index claw being connected to a return pin, the return pin driving back the index claw to its initial position, wherein one end of the second lever and the matching member form a first specific contact and keep a specific actuation relationship, and in that the direction, to which the second lever is able to be moved in order to release the cable, includes at least two different directions; whereby, while the second lever is determined to move in a direction so as to form a second specific contact with the matching member, the index claw rotates to have the second pawl to mesh with another tooth of the ratchet plate, such that a down-shift movement is performed by having the ratchet assembly to rotate toward a second direction.