A particle-optical corrector for eliminating both the third-order aperture aberration and the third-order extra-axial coma, using circular lenses and hexapole fields, includes three coaxially arranged hexapole fields, at least one circular lens doublet being arranged between adjacent hexapole fields and adjusted so that the center hexapole field is imaged on the hexapole fields. Between the hexapole fields, an intermediate plane prevails and the intermediate planes are conjugated with one another. The three hexapole fields are identically oriented in the Larmor reference system with the intensities of the three fields being chosen so that the image aberration coefficient of the astigmatism with three-fold symmetry becomes 0. The corrective contains two hexapole fields, in which the fields of the hexapole field pair are excited anti-symmetrically to one another, and the pairs are in each case arranged around the two intermediate planes. The orientation of the hexapole field pairs is rotated with respect to the orientation defined by the hexapole fields by a sufficient angle so that the extra-axial third order coma is corrected.