  We construct 1/4 BPS configurations, `M-ribbons', in M-theory on T^2, which
give the supertubes and supercurves in type IIA theory upon dimensional
reduction. These M-ribbons are generalized so as to be consistent with the
SL(2,Z) modular transformation on T^2. In terms of the type IIB theory, the
generalized M-ribbons are interpreted as an SL(2,Z) duality family of super
D-helix. It is also shown that the BPS M-ribbons must be straight in one
direction.
