P2P-Grid system provides a framework for converging Grid and peer-to-peer network to deploy large-scale distributed applications. However, Nodes dynamic participation arbitrarily that makes failure more common than in other systems. As the most common technique for fault tolerance, Check pointing-and-Recovery saves application execution state during normal execution and restoring the saved state after a failure to reduce the amount of lost work. In this paper, we propose a Check pointing-and-Recovery architecture for applications restarting as soon as possible on P2P-Grid systems. And failure-detection mechanism is a necessary prerequisite to fault tolerance and fault recovery in P2P-Grid system. To this end, failure-detection mechanisms as an integral part of P2P-Grid system have been well-studied. We investigate how the design of various failure detection algorithms affects their performance in node average failure detection time. We also provide numerical results based on both theoretical analysis and simulations. The evaluated results show improvement of the performance on the basis of the WP failure detection algorithm.