A process for the electroless coating of the surfaces of objects, which comprises the steps or consists of the steps: I. provision of an object composed in each case of at least one polymer, composite, natural material, glass, ceramic and/or metallic material, III. application of an activating layer, V. rinsing of the activating layer, with the activating layer not being removed entirely, VI. contacting and coating of the activated surfaces, which remain after rinsing, with an aqueous composition in the form of a solution, emulsion or suspension to form a subsequent organic layer (= precipitation layer), wherein the activating layer comprises at least one cationic polyelectrolyte having adhesion-promoting chemical groups selected from the group consisting of chemical groups of multifunctional epoxides, isocyanates, primary amines, secondary amines, tertiary amines, quaternary amines, amides, imides, imidazoles, formamides, Michael reaction products, carbodiimides, carbenes, cyclic carbenes, cyclocarbonates, polyfunctional carboxylic acids, amino acids, nucleic acids, methacrylamides, polyacrylic acids, polyacrylic acid derivatives, polyvinyl alcohols, polyphenols, polyols having at least one alkyl and/or aryl radical, caprolactam, phosphoric acids, phosphoric esters, epoxy esters, sulfonic acids, sulfonic esters, vinylsulfonic acids, vinylphosphonic acids, catechol, silanes and the silanols and/or siloxanes formed therefrom, with the use of the cationic polyelectrolytes leading to precipitation of a cationically stabilized dispersion, or wherein the activating layer is formed by a material or mixture selected from the group consisting of chitosan, calcium acetate, calcium formate and mixtures thereof and the aqueous composition for forming a subsequent layer comprises constituents which are precipitable, depositable and/or can be salted out and are anionically, zwitterionically, sterically and/or cationically stabilized, where the anionically and cationically stabilized constituents in the aqueous composition do not interfere with one another, and the dry film formed during this step or later from the subsequent layer or from the activating layer and the subsequent layer has a thickness of at least 1 μm. I. provision of an object composed in each case of at least one polymer, composite, natural material, glass, ceramic and/or metallic material, III. application of an activating layer, V. rinsing of the activating layer, with the activating layer not being removed entirely, VI. contacting and coating of the activated surfaces, which remain after rinsing, with an aqueous composition in the form of a solution, emulsion or suspension to form a subsequent organic layer (= precipitation layer), wherein the activating layer comprises at least one cationic polyelectrolyte having adhesion-promoting chemical groups selected from the group consisting of chemical groups of multifunctional epoxides, isocyanates, primary amines, secondary amines, tertiary amines, quaternary amines, amides, imides, imidazoles, formamides, Michael reaction products, carbodiimides, carbenes, cyclic carbenes, cyclocarbonates, polyfunctional carboxylic acids, amino acids, nucleic acids, methacrylamides, polyacrylic acids, polyacrylic acid derivatives, polyvinyl alcohols, polyphenols, polyols having at least one alkyl and/or aryl radical, caprolactam, phosphoric acids, phosphoric esters, epoxy esters, sulfonic acids, sulfonic esters, vinylsulfonic acids, vinylphosphonic acids, catechol, silanes and the silanols and/or siloxanes formed therefrom, with the use of the cationic polyelectrolytes leading to precipitation of a cationically stabilized dispersion, or wherein the activating layer is formed by a material or mixture selected from the group consisting of chitosan, calcium acetate, calcium formate and mixtures thereof and the aqueous composition for forming a subsequent layer comprises constituents which are precipitable, depositable and/or can be salted out and are anionically, zwitterionically, sterically and/or cationically stabilized, where the anionically and cationically stabilized constituents in the aqueous composition do not interfere with one another, and the dry film formed during this step or later from the subsequent layer or from the activating layer and the subsequent layer has a thickness of at least 1 μm.