The problem of asymptotic stability for autonomous functional differential equations is studied on the basis of the investigation of the roots of the characteristic function. We apply D-decomposition method for obtaining the sharp boundaries of stability domains. We obtain necessary and sufficient conditions of asymptotic stability for two families of linear autonomous differential equations with distributed delay and power kernels. These criteria of stability are formulated in terms of the parameters of the original problem. Based on the criteria, we find absolute stability conditions for each of the families.