The two body systems that work closely together to produce movement in human limbs are:

* Muscular System: Muscles provide the force necessary for movement. They contract and relax, pulling on bones and causing them to move.

* Skeletal System: Bones provide the framework and structure for the body, and act as levers for the muscles to pull on. Joints, where bones meet, allow for movement in different directions.

These two systems work in a coordinated fashion, with the muscular system providing the power and the skeletal system providing the structure and leverage for movement.