In this paper we discuss some moment properties of a symmetric generalized logistic distribution indexed by a shape parameter X and denoted by GL(X X), and show that it is asymptotically normal as X -*• oo, and asymptotically double exponential as X 0. We also show that GL(A, X) can be used to approximate the normal distribution. The proposed approximation is illustrated for specific values of X. AMS 1980 subject classification: Primary 62H10; secondary 65D20. © 1993, Taylor & Francis Group, LLC. All rights reserved.