A method for producing an antiresonant hollow-core fiber comprising a hollow core extending along a fiber longitudinal axis and an inner sheath region which surrounds the hollow core and comprises a plurality of antiresonance elements, comprising the method steps of: (a) providing a cladding tube which comprises a cladding tube inner bore and a cladding tube longitudinal axis along which a cladding tube wall bounded by an inner side and an outer side extends, (b) providing a number of tubular antiresonance element preforms (4; 34), (c) arranging the antiresonance element preforms (4; 34) at target positions on the inner side of the cladding tube wall to form a primary preform (3; 30) which comprises a hollow core region and an inner sheath region, (d) further processing the primary preform (3; 30) to form a secondary preform from which the hollow-core fiber is drawn, wherein the further processing comprises elongation and optionally a single or repeated performance of one or more of the following hot-forming processes: (i) collapse, (ii) collapse and simultaneous elongation, (iii) collapse of additional sheath material, (iv) collapse of additional sheath material and subsequent elongation, (v) collapse of additional sheath material and simultaneous elongation, and (e) drawing the secondary preform to form the hollow-core fiber, wherein, after the elongation according to method step (d), at least a portion of the former tubular antiresonance element preforms (4; 34) of the primary preform (3; 30) has an oval outer cross-sectional shape, with a longest cross-sectional axis A L and a shortest cross-sectional axis A K, wherein the axis length ratio A L /A K is in the range between 1.01 and 1.27, and wherein the shortest cross-sectional axis A K runs in the radial direction when viewed from the cladding tube longitudinal axis, characterized in that during elongation the primary preform (3; 30) is continuously fed to a heating zone at a feed rate, is softened zone by zone in the heating zone, and is withdrawn from the heating zone at a withdrawal rate, wherein the feed rate is set such that a throughput of at least 0.8 g/min and an average dwell time in the heating zone in the range of 5 to 25 min is achieved, and wherein a temperature-controlled heating zone is used, the target temperature of which is maintained to an accuracy of +/- 0.1°C. (a) providing a cladding tube which comprises a cladding tube inner bore and a cladding tube longitudinal axis along which a cladding tube wall bounded by an inner side and an outer side extends, (b) providing a number of tubular antiresonance element preforms (4; 34), (c) arranging the antiresonance element preforms (4; 34) at target positions on the inner side of the cladding tube wall to form a primary preform (3; 30) which comprises a hollow core region and an inner sheath region, (d) further processing the primary preform (3; 30) to form a secondary preform from which the hollow-core fiber is drawn, wherein the further processing comprises elongation and optionally a single or repeated performance of one or more of the following hot-forming processes: (i) collapse, (ii) collapse and simultaneous elongation, (iii) collapse of additional sheath material, (iv) collapse of additional sheath material and subsequent elongation, (v) collapse of additional sheath material and simultaneous elongation, and (i) collapse, (ii) collapse and simultaneous elongation, (iii) collapse of additional sheath material, (iv) collapse of additional sheath material and subsequent elongation, (v) collapse of additional sheath material and simultaneous elongation, and (e) drawing the secondary preform to form the hollow-core fiber, wherein, after the elongation according to method step (d), at least a portion of the former tubular antiresonance element preforms (4; 34) of the primary preform (3; 30) has an oval outer cross-sectional shape, with a longest cross-sectional axis A L and a shortest cross-sectional axis A K, wherein the axis length ratio A L /A K is in the range between 1.01 and 1.27, and wherein the shortest cross-sectional axis A K runs in the radial direction when viewed from the cladding tube longitudinal axis, characterized in that during elongation the primary preform (3; 30) is continuously fed to a heating zone at a feed rate, is softened zone by zone in the heating zone, and is withdrawn from the heating zone at a withdrawal rate, wherein the feed rate is set such that a throughput of at least 0.8 g/min and an average dwell time in the heating zone in the range of 5 to 25 min is achieved, and wherein a temperature-controlled heating zone is used, the target temperature of which is maintained to an accuracy of +/- 0.1°C.