An important need in multi-robot systems is the development of mechanisms that enable robot teams to autonomously generate cooperative behaviors. This paper first briefly presents the Cooperative Multi-robot Observation of Multiple Moving Targets (CMOMMT) application as a rich domain for studying the issues of multi-robot learning of new behaviors. We discuss the results of our hand-generated algorithm for CMOMMT, and then describe our research in generating multi-robot learning techniques for the CMOMMT application, comparing the results to the hand-generated solutions. Our results show that, while the learning approach performs better than random, naive approaches, much room still remains to match the results obtained from the hand-generated approach. The ultimate goal of this research is to develop techniques for multi-robot learning and adaptation that will generalize to cooperative robot applications in many domains, thus facilitating the practical use of multi-robot teams in a wide variety of real-world applications.