To compare two samples of possibly right-censored failure times, a location-scale model, without assuming the distribution form, is considered for the log-transformed data. This new accelerated failure time model is introduced to accommodate the possible heterogeneity between within-treatment variations of the two groups considered. One distinct feature of this model is that, with the presence of heterogeneity, statistical inferences on both location and scale parameters based on log-rank tests or linear rank tests will become inappropriate. In this paper we propose the empirical process approach to construct a regression setup derived from the theory of strong approximation of the Kaplan-Meier product-limit empirical quantile process. A generalized least squares (GLS) estimator is obtained and shown to be semiparametric efficient. Also it is shown that this estimation is adaptive for a special case. At the end, results on the two-sample setting are applied to the K-sample problem.