A method for producing an anti-resonant hollow-core fiber (29; 129) which comprises a hollow core extending along a longitudinal axis of the fiber and a casing region that surrounds the hollow core and comprises a number of anti-resonance elements, comprising the method steps of: (a) providing a primary preform (26; 126) for the hollow-core fiber, which preform has at least one cladding tube comprising a cladding tube inner bore and a cladding tube longitudinal axis along which a cladding tube wall (24; 124) delimited by an inner side and an outer side extends, (b) forming a number of precursors (25a; 25b; 125; 213) for anti-resonance elements (28a; 28b; 128) at target positions of the cladding tube wall (24; 124), and (c) elongating the primary preform (26; 126) to form the hollow-core fiber (29; 129) or further processing the primary preform (26; 126) to form a secondary preform from which the hollow-core fiber is drawn, wherein the further processing comprises carrying out one or more of the following hot-forming processes once or repeatedly: (i) elongation, (ii) collapse, (iii) collapse and simultaneous elongation, (iv) collapse of additional casing material, (v) collapse of additional casing material and subsequent elongation, (vi) collapse of additional casing material and simultaneous elongation, characterized in that the formation of the anti-resonance element precursors (25a; 25b; 125; 213) comprises the formation of elongated pressure chambers (25a; 25b; 125; 213) which each, in the region of the target positions of the anti-resonance elements (28a; 28b; 128), adjoin a wall deformable under pressure and heat, and which, as a result of pressure and heat, when a process according to method step (c) is carried out, cause a bulge of a portion of the deformable wall (21; 22) in the direction of the cladding tube inner bore so as to form an anti-resonance element (29; 129) or a precursor therefor, wherein the portion of the deformable wall is designed as a wall portion of a glass tube (21; 221) and the pressure chambers are each designed as a hollow channel (13; 25a; 25b; 125; 213) which the wall portion of the glass tube (21; 221) adjoins. (a) providing a primary preform (26; 126) for the hollow-core fiber, which preform has at least one cladding tube comprising a cladding tube inner bore and a cladding tube longitudinal axis along which a cladding tube wall (24; 124) delimited by an inner side and an outer side extends, (b) forming a number of precursors (25a; 25b; 125; 213) for anti-resonance elements (28a; 28b; 128) at target positions of the cladding tube wall (24; 124), and (c) elongating the primary preform (26; 126) to form the hollow-core fiber (29; 129) or further processing the primary preform (26; 126) to form a secondary preform from which the hollow-core fiber is drawn, wherein the further processing comprises carrying out one or more of the following hot-forming processes once or repeatedly: (i) elongation, (ii) collapse, (iii) collapse and simultaneous elongation, (iv) collapse of additional casing material, (v) collapse of additional casing material and subsequent elongation, (vi) collapse of additional casing material and simultaneous elongation, (i) elongation, (ii) collapse, (iii) collapse and simultaneous elongation, (iv) collapse of additional casing material, (v) collapse of additional casing material and subsequent elongation, (vi) collapse of additional casing material and simultaneous elongation,