Conformal and quasiconformal realizations of exceptional Lie groups

We present a nonlinear realization of E-8(8) on a space of 57 dimensions, w hich is quasiconformal in the sense that it leaves invariant a suitably def ined "light cone" in R-57. This realization, which is related to the Freude nthal triple system associated with the unique exceptional Jordan algebra o ver the split octonions, contains previous conformal realizations of the lo wer rank exceptional Lie groups on generalized space times, and in particul ar a conformal realization of E-7(7) on R-27 which we exhibit explicitly. P ossible applications of our results to supergravity and M-Theory are briefl y mentioned.