The present invention relates to a process for complete anaerobic digestion of polymer mixtures of the composition: a) 25 to 95% by weight of a polyhydroxyalkanoate selected from the group consisting of poly-4-hydroxybutyrate, poly-3-hydroxybutyrate, poly(3-hydroxybutyrate-co-3-hydroxyvalerate), poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) and poly(3-hydroxybutyrate-co-4-hydroxybutyrate) and b) 5 to 75% by weight of an aliphatic polyester comprising: i) 65 to 100 mol %, based on components i to ii, of succinic acid or of a succinic acid derivative; ii) 0 to 35 mol %, based on components i to ii, of an aliphatic C5-C36-dicarboxylic acid, of a corresponding acid derivative or of a mixture; iii) 98 to 100 mol %, based on components i to ii, of a C2-C8-alkylenediol or C2-C6-oxyalkylenediol; iv) 0 to 2% by weight, based on the polymer obtainable from components i to iii, of at least one polyfunctional compound comprising at least two isocyanate, isocyanurate, oxazoline or epoxide groups or at least three alcohol or carboxylic acid groups.