  The `electromagnetic' $Sl(2;\bZ)$ duality group in spacetime dimension $D=4k$
can be given a Kaluza-Klein interpretation in $D=4k+2$ as the modular group of
a compactifying torus. We show how dyonic $2(k-1)$-branes in $D=4k$ can be
interpreted as self-dual $(2k-1)$-branes in $D=4k+2$ wound around the homology
cycles of the torus. In particular, dyons of the D=4 N=4 heterotic string
theory are interpreted as winding modes of a D=6 self-dual string, while D=8
dyonic membranes are interpreted as wound 3-branes of D=10 IIB superstring
theory. We also discuss the T-dual IIA interpretations of D=8 dyonic membranes.
