Hipparcos trigonometric parallaxes fix distances to individual stars in the Hyades cluster with an accuracy of about 6 percent. We use the Hipparcos and Tycho-2 proper motions, which have a larger relative precision than the Hipparcos trigonometric parallaxes, to derive 3 times more precise distance estimates, by assuming that all members share the same space motion. These so-called secular parallaxes are, as a set, statistically consistent with the Hipparcos parallaxes (Section 6). Table A1 contains, for all 218 members identified by Perryman et al. (1998A&A...331...81P; see also Cat. <J/A+A/331/81>; see Sections 4.1 and 5.1), the trigonometric parallaxes, the Hipparcos and Tycho-2 secular parallaxes, their errors and goodness-of-fit parameters (Sections 2.2 and 5.4), as well as fundamental stellar parameters (Section 9) based on the Hipparcos secular parallaxes and the V-band magnitudes (field H5) and B-V colours (field H37) listed in the Hipparcos Catalogue (1997HIP...C......0E; Cat. <I/239>). Table A2 lists 15 new Hyades candidates (see Sections 4.2 and 5.2) selected by the membership methods developed by de Bruijne (1999MNRAS.306..381D) and Hoogerwerf et al. (1999MNRAS.306..394H) which use proper motion and trigonometric parallax data. Based on photometric, radial velocity, and secular parallax data, we conclude that only one of these stars (HIP 19757) is a likely new member (see Sections 4.2 and 5.2 for details).