A scheduler must consider the heterogeneity and communication delays when scheduling dependent tasks on a grid. The task-scheduling problem is NP-Complete in general, which led us to the development of a heuristic for the associated optimization problem. In this work we present a dynamic adaptive approach to schedule dependent tasks onto a grid based on the Xavantes grid middleware. The developed dynamic approach is applied to the Path Clustering Heuristic, and introduces the concept of rounds, which take turns sending tasks to execution and evaluating the performance of the resources. The adaptive extension changes the size of rounds during the process execution, taking task attributes and resources performance as parameters, and it can be adopted in other task schedulers. The experiments show that the dynamic round-based and adaptive schedule can minimize the effects of performance losses while executing processes on the grid. Copyright © 2007 John Wiley & Sons, Ltd.20910291049Bittencourt, L.F., Madeira, E.R.M., Cicerre, F.R.L., Buzato, L.E., A path clustering heuristic for scheduling task graphs onto a grid (short paper) (2005) Proceedings of the 3rd ACM International Workshop on Middleware for Grid Computing, , Grenoble, FranceCicerre, F.R.L., Madeira, E.R.M., Buzato, L.E., A hierarchical process execution support for grid computing (2006) Concurrency and Computation: Practice and Experience, 18 (6), pp. 581-594Kwok, Y.-K., Ahmad, I., Dynamic critical-path scheduling: An effective technique for allocating task graphs to multiprocessors (1996) IEEE Transactions on Parallel and Distributed Systems, 7 (5), pp. 506-521Yang T, Gerasoulis A. DSC: Scheduling parallel tasks on an unbounded number of processors. IEEE Transactions on Parallel and Distributed Systems 19945(9):951-967Bajaj, R., Agrawal, D.R., Improving scheduling of tasks in a heterogeneous environment (2004) IEEE Transactions on Parallel and Distributed Systems, 15 (2), pp. 107-118Sakellariou, R., Zhao, H., A hybrid heuristic for DAG scheduling on heterogeneous systems (2004) Proceedings of the 13th Heterogeneous Computing Workshop, pp. 111-124. , IEEE Computer Society Press: Los Alamitos, CATopcuoglu, H., Hariri, S., Wu, M.-Y., Performance-effective and low-complexity task scheduling for heterogeneous computing (2002) IEEE Transactions on Parallel and Distributed Systems, 13 (3), pp. 260-274Hagras, T., Janeček, J., An approach to compile-time task scheduling in heterogeneous computing systems (2004) Proceedings of the 33rd International Conference on Parallel Processing Workshops, pp. 182-189. , IEEE Computer Society Press: Los Alamitos, CAFrey, J., Condor DAGMan: Handling inter-job dependencies, , http://www.cs.wisc.edu/condor/dagman, 25 July 2006Prodan, R., Fahringer, T., Dynamic scheduling of scientific workflow applications on the grid: A case study (2005) Proceedings of the 2005 ACM Symposium on Applied computing (SAC'05), pp. 687-694. , ACM Press: New YorkChen, H., Maheswaran, M., Distributed dynamic scheduling of composite tasks on grid computing systems (2002) Proceedings of the 11th IEEE Heterogeneous Computing Workshop, , Fort Lauderdale, U.S.ACooper, K., Dasgupta, A., Kennedy, K., Koelbel, C., Mandal, A., Marin, G., Mazina, M., Dongarra, J., New grid scheduling and rescheduling methods in the GrADS project (2004) Proceedings of the IPDPS Next Generation Software Program - NSFNGS - PI Workshop, pp. 199-206. , IEEE Computer Society Press: Los Alamitos, CAFujimoto, N., Hagihra, K., Near-optimal dynamic task scheduling of precedence constrained coarse-grained tasks onto a computational grid (2003) Second International Symposium on Parallel and Distributed Computing, pp. 80-87. , Ljubljana, SloveniaWolski, R., Spring, N.T., Hayes, J., The network weather service: A distributed resource performance forecasting service for metacomputing (1999) Future Generation Computer Systems, 15 (5-6), pp. 757-768