This paper presents a Process History Capture System (PHCS) as a logging mechanism for distributed long running business processes executing over Delta-Enabled Grid Services (DEGS). A DEGS is a Grid Service with an enhanced interface to access incremental data changes, known as deltas, associated with service execution in the context of global processes. The PHCS captures process execution context and deltas from distributed DEGSs and constructs a global schedule for multiple executing processes, integrating local schedules that are extracted from deltas at distributed sites. The global schedule forms the basis for analyzing data dependencies among concurrently executing processes. The schedule can be used for rollback and also to identify data dependencies that affect the possible recovery of other concurrent processes. This paper presents the design of the PHCS and the use of the PHCS for process failure recovery. We also outline future directions for specification of user-defined semantic correctness.