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-offreedom body. Even in this simple case, and the more so In general multi-body cases. Improvements in adaptive control laws are found to be needed. A new adaptive control law is developed which is applicable to general, rigid, multi-body systems. It is based on the re-interpretatlon of the system dynamics equation as a measurement equation. The adaptive control law is of the "integrated" type; that is, 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. In one numerical example it is shown how a two-armed, nine degreeof-freedom space robot can be controlled nearly as if the mechanical parameters were precisely known.