The FK6 is a suitable combination of the results of the HIPPARCOS astrometry satellite with ground-based data, measured over a long interval of time and summarized mainly in the FK5. Part III of the FK6 (abbreviated FK6(III) ) contains additional fundamental stars with direct solutions. Such direct solutions are appropriate for single stars or for objects which can be treated like single stars.

Part III of the FK6 contains in total 3272 stars. Their ground-based data stem from the bright extension of the FK5 (735 stars), from the catalogue of remaining Sup stars (RSup, 732 stars), and from the faint extension of the FK5 (1805 stars).

From the 3272 stars in Part III, we have selected 1928 objects as `astrometrically excellent stars', since their instantaneous proper motions and their mean (time-averaged) ones do not differ significantly. Hence most of the astrometrically excellent stars are well-behaving `single-star candidates' with good astrometric data. These stars are most suited for high-precision astrometry. On the other hand, 354 of the stars in Part III are Delta-mu binaries in the sense of Wielen et al. (1999, Astron. Astrophys. 346, 675). Many of them are newly discovered probable binaries with no other hitherto known indication of binarity.

The FK6 gives, besides the classical `single-star mode' solutions (SI mode), other solutions which take into account the fact that hidden astrometric binaries among `apparently single-stars' introduce sizable `cosmic errors' into the quasi-instantaneously measured HIPPARCOS proper motions and positions. The FK6 gives, in addition to the SI mode, the `long-term prediction (LTP) mode' and the `short-term prediction (STP) mode'. These LTP and STP modes are on average the most precise solutions for apparently single stars, depending on the epoch difference with respect to the HIPPARCOS epoch of about 1991.