In a distributed, dynamic and volatile operating environment, runtime anomalies occurring in service-oriented systems (SOSs) must be located and fixed in a timely manner in order to guarantee successful delivery of outcomes in response to user requests. Monitoring all component services constantly and inspecting the entire SOS upon a runtime anomaly are impractical due to excessive resource and time consumption required, especially in large-scale scenarios. We present a spectrum-based approach that goes through a five-phase process to quickly localize runtime anomalies occurring in SOSs based on end-to-end system delays. Upon runtime anomalies, our approach calculates the similarity coefficient for each basic component (BC) of the SOS to evaluate their suspiciousness of being faulty. Our approach also calculates the delay coefficients to evaluate each BC's contribution to the severity of the end-to-end system delays. Finally, the BCs are ranked by their similarity coefficient scores and delay coefficient scores to determine the order of them being inspected. Extensive experiments are conducted to evaluate the effectiveness and efficiency of the proposed approach. The results indicate that our approach significantly outperforms random inspection and the popular Ochiai-based inspection in localizing single and multiple runtime anomalies effectively. Thus, our approach can help save time and effort for localizing runtime anomalies occuring in SOSs.