The present invention relates to the use of formaldehyde-free aqueous binders having a broad molecular weight distribution for substrates, said binders comprising (A) from 0 to 100% by weight of an ethylenically unsaturated acid anhydride or ethylenically unsaturated dicarboxylic acid whose carboxylic acid groups can form an anhydride group, or mixtures thereof, (B) from 100 to 0% by weight of an ethylenically unsaturated compound, (C) at least one polyfunctional crosslinker or mixtures thereof, and (D) from 1-80% by weight of an aqueous polymer dispersion, the polymers of A) and B) obtained by free-radical addition polymerization, when classified in a coordinate system by way of their average molecular weight Mw and their polydispersity, being situated in the area above a straight line which is defined by the linear equation y=1.25x+20 000 and has been shifted in y direction parallelwise by at least +3 000, the x axis denoting the weight-average molecular weight and the y axis the polydispersity times 10 000. The invention further relates to the binders themselves and also to their use for, for example, moldings, mats or boards, especially for fibrous and particulate substrates such as fiber webs, glass fibers, rockwool, reclaimed cotton, natural fibers or synthetic fibers.