Unreliable failure detectors are a basic building block of reliable distributed systems. Failure detectors are used to monitor processes of any application and provide process state information. This work presents an Internet Failure Detector Service (IFDS) for processes running in the Internet on multiple autonomous systems. The failure detection service is adaptive, and can be easily integrated into applications that require configurable QoS guarantees. The service is based on monitors which are capable of providing global process state information through a SNMP MIB. Monitors at different networks communicate across the Internet using Web Services. The system was implemented and evaluated for monitored processes running both on single LAN and on PlanetLab. Experimental results are presented, showing the performance of the detector, in particular the advantages of using the self-tuning strategies to address the requirements of multiple concurrent applications running on a dynamic environment.