Abstract: A now interpretation of the NBUE （new better than used in expectation） class of life distributions with absolutely continuous distribution functions is introduced. In effect, a life distribution is NBUE if, arid only if, it is stochastically larger than the equilibrium distribution of the excess life in the renewal process with such an underlying distribution. Based upon this characterization, some applications in reliability and life-testing are proposed. Furthermore, a nonparamctric procedure is also developed to test for the exponentiality against the strict NBUE property.