Summary: Suppose that \(n_ 1\) and \(n_ 2\) independent copies of a coherent system composed of \(m\) components operate in two different environments. All copies are monitored until their failure. The data consist of the lifetimes of all the components which fail before the system and the time to failure of the system which also is the censoring time for the components not yet failed. We propose a class of tests based on the incidence functions of the component failures obtained from the above data for the equality of the joint distributions of the component lifetimes without assuming either the independence of the components within a system or the knowledge of the structure function of the system. The test statistics have asymptotically a chi-squared distribution with \(m\) degrees of freedom. Results of some simulation studies exhibit the closeness of the approximation of the null distribution and the power of these tests for certain coherent structures.