An outline is given of the spin space-group classi cation of quasiperiodic arrangements of spins. It is based on an extension to multicomponent quasiperiodic elds of the Fourierspace approach to crystal symmetry. The classi cation of decagonal spin space groups in two dimensions is given as an example. A group theoretic argument isgiven which isused to determine extinctions in a neutron di raction experiment, associated with a given spin space group. 1. Quasiperiodic Spin Density Fields We consider quasiperiodic arrangements of spins, like the ones shown in Figure 1, described by a spin density eld S(r) which transforms as an axial vector eld under rotations and changes sign under time inversion. The symmetry groups of periodic spin density elds, called spin groups, were treated by Litvin and Opechowski. 1 Janner and Janssen 2 have suggested the possibility of extending the superspace procedure to treat quasiperiodic spin arrangements. Here I outline the symmetry classi cation of quasiperiodic as well as periodic spin density elds using the Fourier-space approach to crystal symmetry 3 which