Multicluster Grids have emerged as major execution environments to solve large-scale compute-intensive applications, with each participating cluster having its own scheduler under different policies. In order to take full advantages of multicluster Grid capability, computer scientists need to deal with how to collaborate practically and efficiently participating autonomic systems to execute Grid-enabled applications. Experiencing various practical applications, we developed a novel execution model called DA-TC (Dynamic Assignment with Task Containers) to improve application execution in a multicluster Grid environment, in terms of application turnaround time and execution reliability. Experiments show that the DA-TC model significantly reduces turnaround time and increases resource utilization for certain applications.