  We study the magnetic excitations on top of the plateaux states recently
discovered in spin-Peierls systems in a magnetic field. We show by means of
extensive density matrix renormalization group (DMRG) computations and an
analytic approach that one single spin-flip on top of $M=1-\frac2N$
($N=3,4,...$) plateau decays into $N$ elementary excitations each carrying a
fraction $\frac1N$ of the spin. This fractionalization goes beyond the
well-known decay of one magnon into two spinons taking place on top of the M=0
plateau. Concentrating on the $\frac13$ plateau (N=3) we unravel the
microscopic structure of the domain walls which carry fractional
spin-$\frac13$, both from theory and numerics. These excitations are shown to
be noninteracting and should be observable in x-ray and nuclear magnetic
resonance experiments.
