Conventional enzyme membrane reactors are not appropriate for a continuous synthesis of macromolecules and simultaneous product release. By immobilizing the enzyme in sufficiently large pores of a membrane an ensemble of miniaturized bioreactors is created. Product molecules are continuously removed from the enzyme by the flow of the reaction mixture across the membrane. Additionally, by varying the flow rate, it ought to be possible to influence the substrate as well as the enzyme-product residence times and thereby the product macromolecule's size. In this paper we present the first results of experiments involving enzymatic 1,4-alpha-glucan synthesis, using sucrose as substrate, maltooligosaccharides (DP 3-6) as primers, and membrane-immobilized amylosucrase. Epoxy groups for a covalent enzyme immobilization were generated on polypropylene microfiltration membranes by heterogeneous photoinitiated graft polymerization of glycidyl methacrylate. The influence of primer concentration and flow rate through the enzyme-membrane on amylosucrase activity, molecule growth, and coupling efficiency for glucose (% of coupled glucose versus free glucose) were investigated. The enzymatically mediated chain elongation of maltooligosaccharides by the successive addition of glucose units was achieved for the first time in a transmembrane process utilizing amylosucrase membranes.