The invention relates to methods for producing crosslinked polyvinyl acetals, according to which a polyvinyl alcohol (A1) containing carboxyl groups is crosslinked by (i) reacting the polymer (A1) with at least one polyaldehyde of formula R.sup.9(CHO).sub.n, and (ii) at least partly esterifying groups of formula (1) and formula (4a) with each other, said steps being performed in any order. The invention further relates to methods for producing crosslinked polyvinyl acetals, according to which a polyvinyl alcohol (A2) is crosslinked by (i) reacting the polymer (A2) with at least one compound of formula (6), (ii) adding at least one compound of formula (4b), (iii) adding a polyaldehyde of formula (5), and (iv) at least partly esterifying groups of formula (1) and structural units derived from the compound of formula (4b) with each other, the radicals R.sup.7, R.sup.8, R.sup.9, R.sup.10, and R.sup.11, and the index n being defined as indicated in the description. Also disclosed are the crosslinked polyvinyl acetals obtained by means of the inventive method and particularly appropriate areas of application of said polymers. ##STR00001##