Process for the production of three-dimensional, self-supporting and/or substrate-supported formed pieces or of structures on surfaces by means of a site-selective solidification of a liquid to pasty, organically modified material within a bath comprising this material by means of two-photon or multiphoton polymerization, whereby the material contains groups or radicals that are available for an inorganic crosslinking or are already inorganically crosslinked, and wherein both an organic radical polymerizable via two-photon or multiphoton polymerization and a biocompatible, biodegradable or bioresorbable radical must be contained in the material, wherein the material comprises an initiator for said two-photon or multiphoton polymerization and one or more components, selected from compounds having an organic radical polymerizable via two-photon or multiphoton polymerization and compounds which carry at least one biocompatible, biodegradable or bioresorbable radical, providing that if at least one purely organic compound which has both an organic radical polymerizable via two-photon or multiphoton polymerization and a biocompatible, biodegradable or bioresorbable radical is present in the material, this compound is selected from among compounds of formula (A)
- R′—CHR″—O—C(O)—CR′″—CH2 (A)
- wherein the radical R′″ is H or CH3 and wherein R′CHR″ is derived from a compound R′—CHR″OH, selected from among
- (a) monosaccharides, selected from the group consisting of aldo- and keto-pentoses, -hexoses and -heptoses with at least one free hydroxyl group, wherein the non-free hydroxyl groups are present in the protected form,
- dimeric, oligomeric or polymeric carbohydrates, which contain at least one of said monosaccharides,
- (b) monomeric or oligomeric or polymeric sugar alcohols, obtainable by means of reduction of the aldehyde or keto group in the molecules mentioned under (a), or
- (c) saturated monomeric, oligomeric or polymeric monohydroxy acids as well as their lactones and lactides, selected from among α-hydroxy acids and ω-hydroxy acids.