The results of a pulsed NMR study of the ²⁷Al resonance in DyAl₂ are presented and discussed. Quadrupole oscillations in the height of the spin-echo versus pulse separation tau have been found. The oscillations have been used to show that the magnetic hyperfine field at the ²⁷Al nuclei makes an angle of about 14.5 degrees with respect to the (001) direction of easy magnetisation. This result is consistent with an NMR signal originating either from within a domain or close to the edge of a narrow domain wall. In addition, a classical analysis of a 90 degrees domain wall in DyAl₂ is presented and used to compute RF enhancement factors eta , both within domain walls. It is shown, for example, that for an enhancement factor eta =500 at a Dy site the ratio of the crystal-field anisotropy to exchange (K/W) is about -0.035. This ratio is approximately six times smaller than a single crystal estimate of about -0.195, thereby implying that the ¹⁶³Dy NMR signal originates from domain walls, moving in regions of defects and imperfections.