This report addresses the problem of active control of large flexible space structures. The current activities and control schemes in this field are briefly reviewed. A direct output feedback control (DOFC) technique is proposed to control the large flexible space structures. Assuming an N-degree-of-freedom system with n collocated sensor and actuator (S/A) pairs, where N is typically much larger than n, the analysis shows that at least the first n lowest critical vibration modes can be controlled with the system remaining stable. A formula for the selection of the feedback control gain matrix is provided. The DOFC approach is also applicable to the systems with certain types of nonlinearities, as well as systems including sensor/actuator dynamics. A simple criterion for selecting the "optimal" location of collocated sensor and actuator pairs is proposed. Numerical examples are given to illustrate the proposed DOFC technique and the "optimal" location criterion.