We present the results of extended monitoring observations in soft X-rays of the bright eclipsing polar (AM Herculis star) HU Aqr. It was observed between 1990 and 1998 by ROSAT for a total of 230ksec using the PSPC and the HRI detectors and by EUVE with the Deep Survey Imager and the Spectrometer for a total of 580ksec. The overall X-ray brightness of HU Aqr varied due to changes of the mass accretion rate by a factor of 40 over that period of time. At all occasions the X-ray light curve was characterized by a marked on-off behavior due to the self-eclipse of the accreting pole. The X-ray light curve showed eclipses by the companion star, the accretion stream and by an accretion curtain raised between the two stars in the binary. Narrow dips prior to the stellar eclipse are caused by the transit of the outer accretion stream. These dips display marked phase shifts, thus indicating a large movement of the threading region, where the stream couples to the magnetic field. These shifts are shown to be related to changes of the mass accretion rate. Correspondingly, the spot longitude varied between 34° and 50°. The X-ray light curves display clear evidence for the presence of an accretion curtain, which is raised all along the ballistic accretion stream down to the region where the bulk of matter couples onto magnetic field lines. A lower limit to the mass accretion rate in the curtain is 6x10–12M☉/yr, which is of order 10% of the total mass accretion rate. A linear fit to all available eclipse egress times yields an updated orbital ephemeris of the system: BJED(T0)=2449217.345872(35)+Ex0.086820416195(47) with T0 the time of eclipse of the white dwarf centre of mass (BJED: barycentric Julian ephemeris time). The inclusion of a quadratic term gives a better fit to the data but is not regarded as indication of a period change or asynchronous rotation but by a migration of the accretion spot over the surface of the white dwarf. For one particular data set obtained in a high accretion state, detailed light curve modeling was possible. The egress from eclipse lasted 1.3s, which constrained the azimuthal extent of the accretion spot to less than 4° or 450km. The spot extended vertically by ≤0.015Rwd. A comparison of the width of the stream dip and the extent of the accretion spot shows, that only the inner 60-80% of the stream are dense enough to fire the soft X-ray engine. During the eclipse, HU Aqr was detected at a flux level of 6x10–14erg/cm/s. The implied X-ray luminosity is LX=2.2x1029erg/s, comparable with X-ray emission from single, late-type, active stars.