We present a study of absorption line-profile variations in early-B type near-main-sequence stars without emission lines. We have surveyed a total of 171 bright stars using the Nordic Optical Telescope (NOTSA), William Herschel Telescope (ING) and Coudé Auxiliary Telescope (ESO). Our sample contains 75% of all O9.5-B2.5 III-V non-emission-line stars brighter than 5.5 mag. We obtained high signal-to-noise, high-resolution spectra of the SiIII λ4560 triplet - for 125 stars of our sample we obtained more than one spectrum - and examined these for pulsational-like line-profile variations and/or structure. We conclude that about half of our sample stars show evidence for line-profile variations (LPV). We find evidence for LPV in about 65% of our sample stars brighter than V=5.5. For stars with rotational broadening V sin i ∼100 km s-1, we find evidence for LPV in about 75% of the cases. We argue that it is likely that these LPV are of pulsational origin, and that hence more than half of the solar-neighbourhood O9.5-B2.5 III-V stars is pulsating in modes that can be detected with high-resolution spectroscopy. We detected LPV in 64 stars previously unknown to be pulsators, and label these stars as new β Cep candidates. We conclude that there is no obvious difference in incidence of (pulsational) LPV for early-B type near-main-sequence stars in binaries or in OB associations, with respect to single field stars.