A central issue in autonomic management is how to coordinate several autonomic management processes, which is assumed to require significant knowledge exchange. This study investigates whether two autonomic control units, which control the same system, can achieve some level of self-coordination with minimal knowledge exchange between them. We present the results from simulations on a model of two autonomous resource controllers influencing the same system. Each of the controllers tries to balance system utility with the cost of resource usage, without the knowledge of the second controller. Simulations indicate that coordination of autonomic management processes is possible, as the system performs close to optimally with minimal knowledge exchange between the two resource controllers.