We monitored the soft X-ray-selected Seyfert galaxy RX J0437.4-4711 with the EUVE satellite continuously for 20 days in 1994 October-November. The Seyfert was detected in the 70-110 Bi range, both in the short-wavelength spectrometer and in the Deep Survey imager. Its light curve shows large-amplitude variability by a factor of 4 over the 20 day period, and a minimum doubling time of 5 hr. Its power spectrum in the frequency range 10(-6.0) to 10(-4.1) Hz is fitted by a power law of slope -1.25 +/- 0.25. A possible period of 0.906 +/- 0.018 days is also apparent in the light curve and power spectrum. This is a timescale that might correspond to orbital motion in the inner accretion disk around a similar to 10(8) M(.) black hole. The divergence of the power at low frequencies indicates that even longer observations in the EUV would be necessary to characterize the variability of the bulk of the Seyfert luminosity. The ROSAT PSPC spectrum from a pointed observation of RX J0437.4-4711 in 1992 September is well fitted by a power law of energy index alpha = 1.56 +/- 0.09 and N-H = (1.01 +/- 0.16) x 10(20) cm(-2). The EUVE spectrum is consistent with these parameters and shows no evidence of emission lines. We also present an IUE spectrum that reveals a flat continuum in nu f(v), and a Ly alpha line at z = 0.052 with FWHM approximate to 4000 km s(-1). In all of its properties, RX J0437.4-4711 appears to be an ordinary Seyfert 1 galaxy.