The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many different spheres affecting human life. By far the most well-known application of logistic distribution is in the logistic regression which is used for modeling categorical response variables. The exponentiated-exponential logistic distribution, a generalization of the logistic distribution is obtained using the technique by Alzaatreh et al. (2013) of mixing two distributions hereafter called as the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum and the distribution of the sample median. For illustrative purposes, a real life data set is considered as an application of the EEL distribution.