We study the electromagnetic mechanism in surface-enhanced Raman scattering (SERS) from random self-affine fractal metal substrates with nanoscale irregularities by means of the rigorous Green's theorem integral equation formulation. The SERS enhancement factor is calculated from the numerical results for the surface electric field intensity at the pump frequency for ensembles of self-affine fractal realizations a few microns wide with decreasing lower scale cutoff. We observe a dramatic increase of the local and average SERS enhancement factors throughout the visible and near infrared when the size of surface irregularities is diminished to a few nanometers. (C) 2002 Elsevier Science B.V. All rights reserved.