This article shows that the likelihood ratio test for the equality of location parameters ofk(k≥ 2) two-parameter exponential distributions with unequal scale parameters, in general, depends on the unknown scale parameters under the null hypothesis. A modification of the likelihood ratio test is suggested, which is applicable to Type II censored or complete data. The suggested test is consistent and asymptotically optimal in the sense of Bahadur efficiency. Fork= 2, the power function of the test is obtained, and the test is shown to be unbiased. A set of data is analyzed.