000 u00b0 1 100 u00b0 c for about 15 seconds for removing the surface layer through gaseous phase oxidation the carbon fibers after gaseous phase oxidation had a modulus of 65 tonf mm 2 increase by 18 a tensile strength of 272 kgf mm 2 and a fiber diameter of 7 7 u03bcm pitch fibers prepared as described in example 1 were rendered infusible and then carbonized at 2 700 u00b0 c the thus obtained carbon fibers had a modulus of 50 tonf mm 2 a tensile strength of 274 kgf mm 2 and a diameter of 9 0 u03bcm these carbon fibers were subjected to oxidation treatment in the same manner as in example 1 to give fibers with the following physical properties a modulus of 60 tonf mm 2 increase by 20 and a tensile strength of 271 kgf mm 2 the fiber diameter was 8 0 u03bcm pitch fibers prepared as described in example 1 were rendered infusible and then carbonized at 2 600 u00b0 c the thus obtained carbon fibers had a modulus of 45 tonf mm 2 a tensile strength of 250 kgf mm 2 and a diameter of 9 4 u03bcm these carbon fibers were subjected to oxidation treatment in the same manner as in example 1 to give fibers with the following physical properties a modulus of 50 tonf mm 2 increase by 11 and a tensile strength of 251 kgf mm 2 the fiber diameter was 8 4 u03bcm pitch fibers prepared as described in example 1 were rendered infusible and then carbonized at 2.