It is shown numerically that the lowest and the highest eigenmodes of the covariant Laplace-operator in an SU(2) gauge field are strongly localized. This phenomenon is explained by connecting it to the well-known Anderson localization problem (electron moving in a random potential). The role of the potential is played by a gauge invariant quantity, the sum over the field strengths of all plaquettes touching a point. Localization for the Dirac-operator is also discussed. ((orig.)).