The paper focuses on indirect adaptive control of space robot manipulators when maneuvering payloads with imperfectly known mechanical parameters. The objective is to estimate system mechanical parameters during the maneuver itself. The system bodies are rigid, and are concatenated by ideal, rotational joints. Existing adaptive control laws are investigated in an application to a rotating, single-degree-of-freedom body. Even in this simple case, and more so in general multibody cases, improvements in adaptive control laws are found to be needed. A new adaptive control law is developed which is applicable to general, rigid, multibody systems. It is based on the reinterpretation of the system dynamic equations as a measurement equation. The adaptive control law is of the "integrated" type, i.e. the estimator part is used to estimate the integrated influence of the system mechanical parameters, rather than the parameters themselves. The controller part (the control law proper) is of the "certainty equivalence" type. For the single-degree-of-freedom case, the system formal solution is presented. Then the parameter estimation process and the control law are separately analyzed to show that the control system output error is globally asymptotically stable, as well as the parameter error, provided the external command input satisfies a persistent excitation condition. In one numerical example it is shown how a two-armed, nine-degree-of-freedom space robot can be controlled almost as if the mechanical parameters were perfectly known.