In this review talk, I would like to report on the proper motion analysis, which has been recently carried out together with M. Soma and M. Yoshizawa: There has been a persistent demand in astronomy for accurate stellar positions and proper motions, which are represented by an inertial reference system constructed on the basis of a set of consistent astronomical constants. In the reference system the precessional constant plays a primary role. In a series of papers Fricke (1967a,b, 1977a,b) has deter­ mined the luni-solar precessional correction to Newcomb's value and the fictitious motion of the equinox, which have been adopted in the "IAU (1976) System of Astronomical Con­ stants". Based on the precessional correction and the equinoctial motion thus established, the fundamental reference system, the FK5 system (Fricke et al. 1988) for positions and proper motions, has been constructed. However, for several years geodetic VLBI (McCarthy & Luzum 1991) and LLR (Williams et at. 1991) observations have been suggesting an additional correction to the luni-solar precessional constant of the IAU (1976) System. That is, these observations indicate the precessional correction of 6. p ~ -0:'30/cent to the FK5 system. But, the observational period of the earth orientation is considered to be still insufficient to separate unambiguously the precessional change of the earth orientation from the nutation with the longest period of 18. 6 years.