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This paper introduces a family of multivariate symmetric distributions, which includes the one with i.i.d. exponential components as its special member. This family, denoted by Fn, is defined as scale mixtures of the uniform distribution on the surface of the l1 unit sphere and studied from several aspects such as distribution functions, probability density functions, marginal and conditional distributions and components' independence. A more general family Tn in which the survival functions are functions in l1 norm and an important subset Dn,∞ of scale mixtures of random vector with i.i.d. exponential components are also discussed. The relationships among these three families and some applications are given. © 1988.