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We undertook a multisite photometric campaign for the Beta Cephei star Nu Eridani. More than 600 hours of differential photoelectric uvyV photometry were obtained with 11 telescopes during 148 clear nights. The frequency analysis of our measurements shows that the variability of Nu Eri can be decomposed into 23 sinusoidal components, eight of which correspond to independent pulsation frequencies between 5 - 8 c/d. Some of these are arranged in multiplets, which suggests rotational m-mode splitting of nonradial pulsation modes as the cause. If so, the rotation period of the star must be between 30 - 60 d. One of the signals in the light curves of Nu Eri has a very low frequency of 0.432 c/d. It can be a high-order combination frequency or, more likely, an independent pulsation mode. In the latter case Nu Eri would be both a Beta Cephei star and a slowly pulsating B (SPB) star. The photometric amplitudes of the individual pulsation modes of Nu Eri appear to have increased by about 20 per cent over the last 40 years. So do the amplitudes of the dominant combination frequencies of the star. Among the latter, we only could identify sum frequencies with certainty, not difference frequencies, which suggests that neither light-curve distortion in its simplest form nor resonant mode coupling are their single cause. One of our comparison stars, Mu Eridani, turned out to be variable with a dominant time scale of 1.62 d. We believe that it is either an SPB star just leaving its instability strip or that its variations are of rotational origin., Comment: 10 pages, 5 figures