We present dyonic multi-membrane solutions of the N = 2 D = 8 supergra
vity theory that serves as the effective field theory of the T-2-compa
ctified type II superstring theory. The 'electric' charge is fractiona
l for generic asymptotic values of an axion field, as for D = 4 dyons.
These membrane solutions are supersymmetric, saturate a Bogomolnyi bo
und, fill out orbits of an Sl(2; Z) subgroup of the type II D = 8 T-du
ality group, and are non-singular when considered as solutions of T-3-
compactified D = 11 supergravity. On K-3 compactification to D = 4, th
e conjectured type II/heterotic equivalence allows the Sl(2; Z) group
to be reinterpreted as the S-duality group of the toroidally compactif
ied heterotic string and the dyonic membranes wrapped around homology
two-cycles of K-3 as S-duals of perturbative heterotic string states.