Hybrid construction machine comprising: a prime mover; a hydraulic pump which is driven by the prime mover; a swing structure; an electric motor for driving the swing structure; a hydraulic motor for driving the swing structure, the hydraulic motor being driven by the hydraulic pump; an electrical storage device which is connected to the electric motor; a swing operating lever device which is operated for commanding the driving of the swing structure; a second hydraulic actuator which is driven by the hydraulic pump and drives a driven part other than the swing structure; a second operating lever device which is operated for commanding the driving of the second hydraulic actuator; and a control device, characterised in that said control device executes control selected from: hydraulic/electric complex swing control for driving the swing structure by total torque of the electric motor and the hydraulic motor by driving both the electric motor and the hydraulic motor when the swing operating lever device is operated; and hydraulic solo swing control for driving the swing structure by the torque of the hydraulic motor alone by driving only the hydraulic motor when the swing operating lever device is operated, and in that: the control device controls drive torque of the electric motor, drive torque of the hydraulic motor and driving force of the second hydraulic actuator so that the relationship between the position or the speed of the second hydraulic actuator and the swing angle or the swing speed of the swing structure when the swing operating lever device and the second operating lever device are operated at the same time during the hydraulic/electric complex swing control is substantially identical with the relationship between the position or the speed of the second hydraulic actuator and the swing angle or the swing speed of the swing structure when the swing operating lever device and the second operating lever device are operated at the same time during the hydraulic solo swing control. a prime mover; a hydraulic pump which is driven by the prime mover; a swing structure; an electric motor for driving the swing structure; a hydraulic motor for driving the swing structure, the hydraulic motor being driven by the hydraulic pump; an electrical storage device which is connected to the electric motor; a swing operating lever device which is operated for commanding the driving of the swing structure; a second hydraulic actuator which is driven by the hydraulic pump and drives a driven part other than the swing structure; a second operating lever device which is operated for commanding the driving of the second hydraulic actuator; and a control device, characterised in that said control device executes control selected from: hydraulic/electric complex swing control for driving the swing structure by total torque of the electric motor and the hydraulic motor by driving both the electric motor and the hydraulic motor when the swing operating lever device is operated; and hydraulic solo swing control for driving the swing structure by the torque of the hydraulic motor alone by driving only the hydraulic motor when the swing operating lever device is operated, and in that: the control device controls drive torque of the electric motor, drive torque of the hydraulic motor and driving force of the second hydraulic actuator so that the relationship between the position or the speed of the second hydraulic actuator and the swing angle or the swing speed of the swing structure when the swing operating lever device and the second operating lever device are operated at the same time during the hydraulic/electric complex swing control is substantially identical with the relationship between the position or the speed of the second hydraulic actuator and the swing angle or the swing speed of the swing structure when the swing operating lever device and the second operating lever device are operated at the same time during the hydraulic solo swing control. hydraulic/electric complex swing control for driving the swing structure by total torque of the electric motor and the hydraulic motor by driving both the electric motor and the hydraulic motor when the swing operating lever device is operated; and hydraulic solo swing control for driving the swing structure by the torque of the hydraulic motor alone by driving only the hydraulic motor when the swing operating lever device is operated, and in that: the control device controls drive torque of the electric motor, drive torque of the hydraulic motor and driving force of the second hydraulic actuator so that the relationship between the position or the speed of the second hydraulic actuator and the swing angle or the swing speed of the swing structure when the swing operating lever device and the second operating lever device are operated at the same time during the hydraulic/electric complex swing control is substantially identical with the relationship between the position or the speed of the second hydraulic actuator and the swing angle or the swing speed of the swing structure when the swing operating lever device and the second operating lever device are operated at the same time during the hydraulic solo swing control.