This paper checks on the roles of metallicity and evolutionary age in the appearance of the so-called Be phenomenon. Slitless CCD spectra were obtained covering the bulk of the Small Magellanic Cloud. For Halpha line emission twice as strong as the ambient continuum, the survey is complete to spectral type B2/B3 on the main sequence. About 8120 spectra of 4437 stars were searched for emission lines in 84 open clusters. 370 emission-line stars were found, among them at least 231 near the main sequence. For 176 of them, photometry could be found in the OGLE database. For comparison with a higher-metallicity environment, the Galactic sample of the photometric Halpha survey by McSwain & Gies (2005) was used. Among early spectral sub-types, Be stars are more frequent by a factor 3-5 in the SMC than in the Galaxy. The distribution with spectral type is similar in both galaxies, i.e. not strongly dependent on metallicity. The fraction of Be stars does not seem to vary with local star density. The Be phenomenon mainly sets in towards the end of the main-sequence evolution (this trend may be more pronounced in the SMC); but some Be stars already form with Be-star characteristics. In all probability, the fractional critical angular rotation rate, omc, is one of the main parameters governing the occurrence of the Be phenomenon. If the Be character is only acquired during the course of evolution, the key circumstance is the evolution of omc, which not only is dependent on metallicity but differently so for different mass ranges.
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