The present invention relates to a liquid resin intended more particularly for the sizing of mineral fibers which exhibits a dilutability in water at 20.degree. C. at least equal to 1 000% and a level of free formaldehyde preferably of less than 0.4%, expressed as total weight of liquid, this resin being characterized in that it is composed essentially of condensates obtained from a phenolic compound, from formaldehyde and from an aminoalcohol according to the Mannich reaction.The invention also relates to a sizing composition including said resin, to the mineral fibers sized by means of this composition and to the products formed from the mineral fibers, in particular for thermal and/or sound insulation.