Existing theoretical approaches to polymer adsorption on heterogeneous surfaces are applied to the problems of polyelectrolyte and polyampholyte adsorption on randomly charged surfaces. Also, analytical estimates are developed for the critical pH at which weakly charged polyelectrolytes and globular proteins start forming soluble complexes. Below a critical salt concentration, soluble complexes form "on the wrong side" of the protein isoelectric point due to the heterogeneity of the protein surface charge distribution. The analytical estimates are consistent with experimental data on soluble complexes in mixtures of gum arabic and whey protein isolate. (C) 2003 American Institute of Physics.