We have acquired between 127 and 150 h of time-resolved multicolour photometry for each of the three β Cephei stars IL Vel, V433 Car and KZ Mus over a time span of four months from two observatories. All three objects are multiperiodic with at least three modes of pulsation. Mode identification from the relative colour amplitudes is performed. We obtain unambiguous results for the two highest-amplitude modes of IL Vel (both are ℓ = 1) and the three strongest modes of KZ Mus (ℓ = 2, 0 and 1), but none for V433 Car. Spectroscopy shows the latter star to be a fast rotator (v sin i = 240km/s), whereas the other two have moderate v sin i (65 and 47 km/s, respectively). We performed model calculations with the Warsaw-New Jersey stellar evolution and pulsation code. We find that IL Vel is an object of about 12 M ⊙ in the second half of its main sequence evolutionary track. Its two dipole modes are most likely rotationally split components of the mode originating as p1 on the ZAMS; one of these modes is m = 0. V433 Car is suggested to be an unevolved 13 M ⊙ star jus
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