Process for producing a polymer consisting of a linear main chain of beta-D- -glucopyranosyl units having a single beta-D-glucopyranosyl unit linked to a beta-D-glucopyranosyl unit of the linear main chain with an average branching degree of about 0.3, said process comprising the steps of: (i) culturing in a medium a genetically modified microorganism capable of producing a polymer consisting of a linear main chain of beta-D- -glucopyranosyl units having a single beta-D-glucopyranosyl unit linked to a beta-D-glucopyranosyl unit of the linear main chain with an average branching degree of about 0.3, wherein the genetically modified microorganism - compared to a non-modified control microorganism of the same strain - has increased activity of at least two gene products selected from the group consisting of phosphoglucomutase with a SEQ ID NO:29 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:29 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:29, UTP-glucose-1-phosphate uridyltrasferase with a SEQ ID NO:41 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:41 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:41, branching enzyme with a SEQ ID NO:2 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:2 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:2; under conditions allowing said microorganism to produce said polymer; wherein an increased activity of the respective gene product is achieved by introducing into the microorganism genes in multiple copies for the respective gene product, (ii) optionally recovering said polymer from the medium, wherein said microorganism is Schizophyllum and wherein said polymer is schizophyllan. (i) culturing in a medium a genetically modified microorganism capable of producing a polymer consisting of a linear main chain of beta-D- -glucopyranosyl units having a single beta-D-glucopyranosyl unit linked to a beta-D-glucopyranosyl unit of the linear main chain with an average branching degree of about 0.3, wherein the genetically modified microorganism - compared to a non-modified control microorganism of the same strain - has increased activity of at least two gene products selected from the group consisting of phosphoglucomutase with a SEQ ID NO:29 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:29 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:29, UTP-glucose-1-phosphate uridyltrasferase with a SEQ ID NO:41 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:41 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:41, branching enzyme with a SEQ ID NO:2 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:2 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:2; under conditions allowing said microorganism to produce said polymer; wherein an increased activity of the respective gene product is achieved by introducing into the microorganism genes in multiple copies for the respective gene product, phosphoglucomutase with a SEQ ID NO:29 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:29 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:29, UTP-glucose-1-phosphate uridyltrasferase with a SEQ ID NO:41 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:41 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:41, branching enzyme with a SEQ ID NO:2 or a polypeptide sequence which is at least 95% identical to SEQ ID NO:2 and which have at least 80% of the enzymatic activity of the polypeptide according to SEQ ID NO:2; (ii) optionally recovering said polymer from the medium, wherein said microorganism is Schizophyllum and wherein said polymer is schizophyllan.