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The evolutionary status of Be-type stars remains unclear, with both single-star and binary pathways having been proposed. Here, VFTS spectroscopy of 73 Be-type stars, in the spectral-type range, B0--B3, is analysed to estimate projected rotational velocities, radial velocities and stellar parameters. They are found to be rotating faster than the corresponding VFTS B-type sample but simulations imply that their projected rotational velocities are inconsistent with them all rotating at near critical velocities. The de-convolution of the projected rotational velocities estimates leads to a mean rotational velocity estimate of 320-350 km/s, approximately 100 km/s larger than that for the corresponding B-type sample. There is a dearth of targets with rotational velocities less than 0.4 of the critical velocity, with a broad distribution reaching up to critical rotation. Our best estimate for the mean or median of the rotational velocitiy is 0.68 of the critical velocity. Rapidly-rotating B-type stars are more numerous than their Be-type counterparts, whilst the observed frequency of Be-type stars identified as binary systems is significantly lower than that for normal B-type stars, consistent with their respective radial-velocity dispersions. The semi-amplitudes for the Be-type binaries are also smaller. Similar results are found for a SMC Be-type sample centred on NGC346 with no significant differences being found between the two samples. These results are compared with the predictions of single and binary stellar evolutionary models for Be-type stars. Assuming that a single mechanism dominated the production of classical Be-type stars, our comparison would favour a binary evolutionary history.