A development of balloon theory and an analysis of the performance of balloons as vehicles on Mars. The authors present a general theory that describes the behavior of extensible balloons and three classes of nonextensible balloons. With reasonable assumptions concerning the Martian atmosphere and the success of certain research efforts, the theory indicates that balloons can perform varied tasks on Mars. The Report summarizes present knowledge of the atmosphere of Mars and gives numerical examples for balloon performance on Mars. Close attention is given to the choice of a buoyant gas, fabrics, and other necessary elements in balloon-system design. Appendices deal with balloon temperature, methods for gas transport from Earth, and the dynamics of the rising balloon.