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ASTRONOMY AND ASTROPHYSICS Study of an unbiased sample of B stars observed with Hipparcos: the discovery of a large amount of new Slowly Pulsating B Stars Abstract. We present a classiication of 267 new variable B-type stars discovered by Hipparcos. We have used two diierent classiication schemes and they both result in only a few new Cephei stars, a huge number of new Slowly Pulsating B stars, quite some supergiants with Cyg-type variations and variable CP stars, and further some new periodic Be stars and eclipsing binaries. Our results clearly point out the biased nature towards short-period variables of earlier, ground-based surveys of variable stars. The position of the new Cephei stars and Slowly Pulsating B stars in the HR diagram is determined by means of Geneva photometry and is confronted with the most recent calculations of the instability strips for both groups of variables. We nd that the new Cephei stars are situated in the blue part of the instability strip and that the new Slowly Pulsating B stars almost fully cover the theoretical instability domain determined for such stars. The supergiants with Cyg-type variations are situated between the instability strips of the Cephei and the Slowly Pulsating B stars on the one hand and previously known supergiants that exhibit microvariations on the other hand. This suggests some connection between the variability caused by the mechanism acting in a zone of partially ionised metals and the unknown cause of the variations in supergiants.