We give a classification of all multiple intersections of D-branes in
ten dimensions and M-branes in eleven dimensions that correspond to th
reshold BPS bound states. The residual supersymmetry of these composit
e branes is determined. By dimensional reduction composite p-branes in
lower dimensions can be constructed. We emphasize in dimensions D gre
ater than or equal to 2 those solutions which involve a single scalar
and depend on a single harmonic function. For these extremal branes we
obtain the strength of the coupling between the scalar and the gauge
field. In particular, we give a D-brane and M-brane interpretation of
extreme p-branes in two, three and four dimensions. (C) 1997 Elsevier
Science B.V.