The load and data management in Grid computing infrastructure is complex. A grid computing application is divided into several sets of tasks between which there are precedence relations. Such relationship poses a challenge for the tasks assignment witch have to minimize the average response time of applications and reduce the communication cost. This problem becomes much more complex when the tasks manipulate replicated data because we have to manage their consistency. In this paper, we propose a tasks assignment and data consistency management strategy based on Tasks and Data Replication. Our main goals are:(a) reducing, the average response time of tasks submitted to the System,(b) respecting the constraints of dependency between tasks,(c) managing data consistency, and,(d) reducing communication costs.