Many companies offer physical products combined with on-line services. For example, product configuration, ordering, order tracking, and payments can be done on-line.The service part of the total offering (the composition) istypically composed of services offered by providers whereperformance of both the composition (provided by the company) and the input services (obtained from providers) isgoverned by service level agreements (SLAs). The goal of our approach is to diagnose the performance of an on-lineservice composition in terms of the performance of on-lineinput services, with respect to the performance indicatorsmentioned in the SLAs, and to do this in real-time.Classical SLA monitoring techniques are batch-orientedand are not usable in the highly dynamic environment ofWeb service provision, where provider relations may changeeven during service delivery. Our techniques use real-timeanalysis of log files to trace and diagnose performance on-the-fly. Current Web service monitoring techniques do notrelate a composite service to its components, as needed toprovide diagnostic information. Furthermore, current approaches do not take into account that the dependency of acomposition on its components varies for different attributes (such as cost and response time). In this paper we propose to extend our previous research in this area by lifting a number of simplifying assumptions to make the approach applicable in real-life, and by extending our study to frequently used SLAs in practice.