An application of extremal optimization algorithm for mapping Java program components on clusters of Java Virtual Machines (JVMs) is presented. Java programs are represented as Directed Acyclic Graphs in which tasks correspond to methods of distributed active Java objects that communicate using the RMI mechanism. The presented probabilistic extremal optimization approach is based on the local fitness function composed of two sub-functions in which elimination of delays of task execution after reception of required data and the imbalance of tasks execution in processors are used as heuristics for improvements of extremal optimization solutions. The evolution of an extremal optimization solution is governed by task clustering supported by identification of the dominant path in the graph. The applied task mapping is based on dynamic measurements of current loads of JVMs and inter-JVM communication link bandwidth. The JVM loads are approximated by observation of the average idle time that threads report to the OS. The current link bandwidth is determined by observation of the performed average number of RMI calls per second.