In this thesis an alternative production mode for producing the bioplastics poly[(R)-3-hydroxybutyrate] (P3HB) was developed. The work can be divided into two parts. In the first part, a process for the production of the P3HB from the agro-industrial by-product chicory roots was developed. The inulin of the roots was extracted and hydrolysed enzymatically. The obtained hydrolysate was then used as a fermentation substrate for three P3HB-producing Cupriavidus necator strains. All three organisms produced polymers which were extracted and several thermo-mechanical parameters determined. The polymer properties were showed that these polymers can be used as blend component for packaging material made for the locally produced vegetables. In the second part, a general process setup for the production of P3HB from frequently occurring agro-industrial by-products with a low carbon concentration was established, in order to make these residues amenable to highly productive industrial P3HB fermentations. In the developed membrane bioreactor, the cells were retained within a constant volume inside the bioreactor using an external microfiltration module. A synthetic medium containing a low glucose concentration was continuously fed to Cupriavidus necator DSM 545, which converted the sugar to P3HB. With the optimized setup a very high productivity, high cell density with a high polymer fraction, and a good yield were reached. This approach creates the possibility for bioplastic production from a range of cheap and easily available substrates, for which only anaerobic digestion was cost-competitive until now.