Statistically structured biodegradable aliphatic-aromatic polyesteramides, comprising the following monomers: aliphatic dialcohols such as ethylene glycol, diethylene glycol, 1-4-butandiol, 1,3-propandiol, 1,6-hexandiol or cycloaliphatic diols such as cyclohexandimethanol and/or aliphatic dicarboxylic acid such as oxalic acid, succinic acid, adipic acid, etc. also in the form of the corresponding esters (methyl, ethyl, etc.) and/or aromatic dicarboxylic acids such as terephthalic acid, isophthalic acid, phthalic acid, etc. also in the form of the corresponding esters (methy, ethyl, etc.) and/or hydroxycarboxylic acids and lactone such as caprolactone, etc. and/or amino alcohols such as ethanolamine, propanolamine, etc. and/or cyclic lactam such as .epsilon.-caprolactam or laurine lactam, etc. and/or .omega.-aminocarboxylic acids such as aminocaproic acid etc. and/or mixtures (1:1 salts) of dicarboxylic acids such as adipic acid, succinic acid, terephthalic acid, etc. and diamines such as hexamethylene diamine, diamino butane, etc., wherein said polyesteramides contain up to 70 mol % aromatic dicarboxylic acids (in relation to the amount of acids).