Detection conditions of specific classes of faults have recently been studied by many researchers. Under the assumption that at most one of these faults occurs in the software under test, these fault detection conditions were mainly used in two ways. First, they were used to develop test case selection strategies for detecting corresponding classes of faults. Second, they were used to study fault class hierarchies, where a test case that detects a particular class of faults can also detect some other classes of faults. In this paper, we study detection conditions of double faults. Besides developing new test case selection strategies and studying new fault class hierarchies, our analysis provides further insights to the effect of fault coupling. Moreover, these fault detection conditions can be used to compare effectiveness of existing test case selection strategies (which were originally developed for the detection of single occurrence of certain classes of faults) in detecting double faults that may be present in the software.