A composite connector comprising: a first module comprising a first housing in which a first connector is exposed from a distal end thereof, and a second housing comprising a second connector; and a second module including a third connector, a fourth housing comprising the third connector, and a third housing including a fourth connector, the third connector being configured to be mated with and electrically connected to the first connector, and the fourth connector being configured to be mated with and electrically connected to the second connector, the composite connector being configured so that the second and fourth connectors (23,33) are mated with each other in a state in which a bulging part that is formed in the second housing is mated with a recessed part that is formed in the third housing, wherein the mating direction of the first connector of the first module and the third connector of the second module differs from the mating direction of the second connector of the first module and the fourth connector of the second module, wherein the second housing is rotatable about the first housing, so that after the first connector of the first module is mated with the third connector of the second module, the second housing is rotated around the first housing of the first module so that the bulging part of the second housing of the first module is mated with the recessed part of the third housing of the second module, characterized in that the first housing has a hollow columnar shape and comprises annular flange parts projecting in a radial direction; the second housing includes a first case and a second case; wherein the first case comprises a roughly semicircular first cut-out part and a roughly semicircular third cut-out part; wherein the second case comprises an arm part having a roughly semi-cylindrical shape; wherein a part between the flange parts of the first housing is accommodated in the first cut-out part and the third cut-out part of the second housing and the first housing is accommodated inside the arm part. a first module comprising a first housing in which a first connector is exposed from a distal end thereof, and a second housing comprising a second connector; and a second module including a third connector, a fourth housing comprising the third connector, and a third housing including a fourth connector, the third connector being configured to be mated with and electrically connected to the first connector, and the fourth connector being configured to be mated with and electrically connected to the second connector, the composite connector being configured so that the second and fourth connectors (23,33) are mated with each other in a state in which a bulging part that is formed in the second housing is mated with a recessed part that is formed in the third housing, wherein the mating direction of the first connector of the first module and the third connector of the second module differs from the mating direction of the second connector of the first module and the fourth connector of the second module, wherein the second housing is rotatable about the first housing, so that after the first connector of the first module is mated with the third connector of the second module, the second housing is rotated around the first housing of the first module so that the bulging part of the second housing of the first module is mated with the recessed part of the third housing of the second module, characterized in that the first housing has a hollow columnar shape and comprises annular flange parts projecting in a radial direction; the second housing includes a first case and a second case; wherein the first case comprises a roughly semicircular first cut-out part and a roughly semicircular third cut-out part; wherein the second case comprises an arm part having a roughly semi-cylindrical shape; wherein a part between the flange parts of the first housing is accommodated in the first cut-out part and the third cut-out part of the second housing and the first housing is accommodated inside the arm part.