The logistic family of distributions belongs to the class of important families
in Probability and Statistics. However, the goodness-of-fit tests for the composite hypothesis on belonging to the logistic family with unknown location parameter against the general alternatives are almost unexplored. We propose two new goodness-of-fit tests, the integral and the Kolmogorov type, based on the recent characterization of logistic family due to Hu and Lin. They are build using the U-empirical measures. We discuss asymptotic properties of new tests such as their limiting distributions and large deviations, and calculate their local Bahadur efficiency against natural alternatives. Conditions of local asymptotic
optimality of new tests are also explored.