  Spin wave nonreciprocity in domain walls (DWs) allows for unidirectional
signal processing in reconfigurable magnonic circuits. Using scanning
transmission x-ray microscopy (STXM), we examined coherently-excited magnons
propagating in Bloch-like DWs in amorphous Fe/Gd multilayers with perpendicular
magnetic anisotropy (PMA). Near 1 GHz we detected magnons with short
wavelengths down to $\lambda = 281$ nm in DWs whose minimum width amounted to
$\delta_{\rm DW} = 52$ nm. Consistent with micromagnetic simulations, the STXM
data reveal their nonreciprocal magnon band structures. We identified Bloch
points which disrupted the phase evolution of magnons and induced different
$\lambda$ adjacent to the topological defects. Our observations provide direct
evidence of nonreciprocal spin waves within Bloch-like DWs, serving as
programmable waveguides in magnonic devices with directed information flow.
