Web services have become a prominent paradigm for building of both inter and intra-enterprise business processes. These processes are composed from existing Web services based on defined requirements. Standards and techniques have been developed to aid in the dynamic composition of services. However, these approaches are limited when it comes to the handling of unexpected events. This dissertation presents the results of experiments that investigated numerous problems related to Web service composition processes. Based on the investigation, a fault taxonomy was formulated. Faults were grouped into three broad categories, each representing a distinct problem stage. The investigation into faults gave rise to the issue of fault recovery and continued process execution. A list of requirements for self-healing Web service composition was identified, while a new self-healing cycle was exploited based on the MAPE cycle (Monitor, Analyzer, Planner, Executive). The proposed self-healing composition cycle consists of three modules: Plan Generation Module, Plan Execution Module and Failure Analysis Module. The plan execution module, consisting of the execution and run-time monitoring phases, and the failure analysis module, consisting of the analysis and sensemaking phases, were found to be vital to self-healing Web service composition. Self healing Web service composition and the goal of self-healing were achieved through the use of Hierarchical Task Network (HTN) planning systems.