This paper is on autonomous three-dimensional maneuvering of teams of fixed-wing unmanned aerial vehicles (UAVs), cooperating with each other during the mission flight. The goal is to design a distributed control scheme that preserves the shape of the UAV team formation by keeping the inter-agent distances constant during arbitrary maneuvers. The paper considers the dynamic characteristics and constraints of the UAVs resulting from being fixed-wing; and proposes a Lyapunov analysis based individual UAV control design to complement the distributed control scheme. After presentation of formal design of the distributed control scheme and individual UAV controllers, simulation results are provided demonstrating effectiveness of the proposed control design.