In May 1994 the BL Lac object PKS 2155-304 was observed continuously for ~10 d with IUE and EUVE and for 2 d with ASCA, as well as with ROSAT and with ground- based radio, IR, and optical telescopes. The light curves show a well-defined X-ray flare (x2 increase in 1/2 d, with similar decay) followed by a broader, lower amplitude EUV flare ~1 day later, and a broad, low-amplitude UV flare ~2 d later (amplitude ~35%, duration >2 d). In the preceding week there was at least one X-ray flare of comparable amplitude or perhaps ongoing stochastic X-ray variations. An extremely rapid change in UV flux was seen at the beginning of the IUE observation. Assuming the central X-ray, EUV, and UV events are associated, the lags, the decrease of amplitude with wavelength, and the broadening of the temporal profile with wavelength are all qualitatively as expected for synchrotron emission from an inhomogeneous relativistic jet. We can rule out a Fermi-type shock acceleration event or a pair cascade in a homogeneous synchrotron-emitting region. A homogeneous region is still possible if there was an instantaneous (t<<hours) injection of high energy electrons that emit first at X-ray energies. Alternatively, the data are consistent with a compression wave or other disturbance crossing a region with stratified particle energy distributions (e.g., behind a shock front and/or in an inhomogeneous jet). The present light curves are in sharp contrast to November 1991, when the amplitude was wavelength independent and the UV lagged the X-rays by less than ~3 hours. This means that the origin of rapid multiwavelength variability in this blazar is complex, involving at least two different modes. (abbreviated abstract)
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