A curable formaldehyde-free binding composition for use with fiberglass is provided. Such curable composition comprises an acid-catalyzed reaction product of an aldehyde or ketone with a multihydric alcohol. When heated, the composition forms polyacetal or polyketal that undergoes curing to form a water-insoluble resin binder which exhibits good adhesion to glass. In a preferred embodiment, maleic anhydride initially serves as a catalyst and subsequently enters into a cross-linking reaction during curing to form a poly(ester-acetal). Also, in a preferred embodiment, the fiberglass is in the form of building insulation. In other embodiments the product can be a microglass-based substrate for use in a printed circuit board, battery separator, filter stock, or reinforcement scrim.