We re-examine the question of heterotic/heterotic string duality in si
x dimensions and argue that the E(8) x E(8) heterotic string, compacti
fied on K3 with equal instanton numbers in the two E(8)'s, has a self-
duality that inverts the coupling, dualizes the antisymmetric tensor,
acts non-trivially on the hypermultiplets, and exchanges gauge fields
that can be seen in perturbation theory with gauge fields of a non-per
turbative origin. The special role of the symmetric embedding of the a
nomaly in the two E(8)'s can be seen from held theory considerations o
r from an eleven-dimensional point of view, The duality can be deduced
by looking in two different ways at eleven-dimensional M-theory compa
ctified on K3 x S-1/Z(2).