  We use exact diagonalization and the modified Lanczos method to study the
finite energy and finite momentum spectral weight of the longitudinal and
transverse spin excitations of the anisotropic zig-zag ladder. We find that the
spin excitations form continua of gapless or gapped spinons in the different
regions of the phase diagram. The results obtained are consistent with a
picture previously proposed that in the anisotropic case there is a transition
from a gapped regime to a gapless regime, for small interchain coupling. In
this regime we find a sharp low-energy peak in the structure function for the
transverse spin excitations, consistent with a finite stiffness.
