The Hipparcos Catalogue (Cat. I/239) contains members of nearby OB associations brighter than 12th magnitude in V. However, membership lists are complete only to magnitude V=7.3. In this paper we discuss whether proper motions listed in the `Astrographic Catalogue+Tycho' reference catalogue (ACT, Cat. I/246) and the Tycho Reference Catalogue (TRC, Cat. I/250), which are complete to V~10.5mag, can be used to find additional association members. Proper motions in the ACT/TRC have an average accuracy of ~3mas/yr. We search for ACT/TRC stars which have proper motions consistent with the spatial velocity of the Hipparcos members of the nearby OB associations already identified by de Zeeuw et al. (1999, Cat. J/AJ/117/354). These stars are first selected using a convergent-point method, and then subjected to further constraints on the proper-motion distribution, magnitude and colour to narrow down the final number of candidate members. Monte Carlo simulations show that the proper-motion distribution, magnitude, and colour constraints remove ~97% of the field stars, while at the same time retain more than 90% of the cluster stars. The procedure has been applied to five nearby associations: the three subgroups of Sco OB2, plus Per OB3 and Cep OB6. In all cases except Cep OB6, we find evidence for new association members fainter than the completeness limit of the Hipparcos Catalogue. However, narrow-band photometry and/or radial velocities are needed to pinpoint the cluster members, and to study their physical characteristics.