We present the data and preliminary analysis for a series of 90 ROSAT HRI and two ASCA observations of the broad-line radio galaxy 3C 390.3. These data were obtained during the period 1995 January 2 to October 6 as part of an intensive multiwavelength monitoring campaign. The soft X-ray flux in the ROSAT band varied by nearly a factor of 4 during the campaign, and the well-resolved light curve shows several distinct features. Several large-amplitude flares were observed, including one in which the flux increased by a factor of about 3 in 12 days. Periods of reduced variability were also seen, including one nearly 30 days long. While the HRI hardness ratio decreased significantly, it is apparently consistent with that expected from the detector during the monitoring period. The two ASCA observations were made on 1995 January 15 and May 5. The 0.5-10.0 keV spectra can be described adequately by an absorbed power law. There is no evidence for a soft excess in the ASCA spectra, indicating that the ROSAT HRI is sampling variability of the X-ray power law. A broad iron line was observed in a longer 1993 ASCA observation, and while there is statistical evidence that the line is present in the 1995 spectra, it could not be resolved clearly. There is evidence, significant at greater than 90% confidence, that the photon index changed from 1.7 to 1.82 while the flux increased by 63%. The spectral change can be detected in the spectra below 5 keV, indicating that the origin cannot be a change in the ratio of reflected to power-law flux. A compilation of results from ASCA and Ginga observations show that on long timescales, the intrinsic photon index is correlated with the flux. © 1997. The American Astronomical Society. All rights reserved.