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Context. The Ap stars that rotate extremely slowly, with periods of decadesto centuries, represent one of the keys to the understanding of the processesleading to the differentiation of stellar rotation.  Aims. We characterise the variations of the magnetic field of the Ap star HD50169 and derive constraints about its structure.  Methods. We combine published measurements of the mean longitudinal field<Bz> of HD 50169 with new determinations of this field moment from circularspectropolarimetry obtained at the 6-m telescope BTA of the SpecialAstrophysical Observatory of the Russian Academy of Sciences. For the meanmagnetic field modulus <B>, literature data are complemented by the analysis ofESO spectra, both newly acquired and from the archive. Radial velocities arealso obtained from these spectra.  Results. We present the first determination of the rotation period of HD50169, Prot = (29.04+/-0.82) y. HD 50169 is currently the longest-period Apstar for which magnetic field measurements have been obtained over more than afull cycle. The variation curves of both <Bz> and <B> have a significant degreeof anharmonicity, and there is a definite phase shift between their respectiveextrema. We confirm that HD 50169 is a wide spectroscopic binary, refine itsorbital elements, and suggest that the secondary is probably a dwarf star ofspectral type M.  Conclusions. The shapes and mutual phase shifts of the derived magneticvariation curves unquestionably indicate that the magnetic field of HD 50169 isnot symmetric about an axis passing through its centre. Overall, HD 50169appears similar to the bulk of the long-period Ap stars.

The variation of the magnetic field of the Ap star HD~50169 over its 29 year rotation period