Kossel interferences of CoKα- and NiKα-radiation are observed, using a 30 keV electron beam to excite fluorescence radiation inside a two-dimensional Al70Co15Ni15 quasicrystal. The reflections detected allow a determination of lattice parameters and crystal orientation. Furthermore some of the Kossel lines possess a fine structure as is known from periodical crystals. Especially the occurrence of the “light-dark” contrast is an indicator for a constant phase shift between the primary and diffracted X-rays, and for the dynamical character of the process, respectively.