We present an analysis of 40 cool helium-rich white dwarfs found in the Hamburg/ESO survey. They were selected for follow-up spectroscopy because of their U-B colour below -0.18, the absence of strong absorption lines, and a continuum shape similar to that of a quasar. Effective temperatures for individual stars were determined by fitting model atmospheres of nearly pure helium with a small admixture of hydrogen. As a consequence of the selection criteria all but one sample stars have T_eff_ below 20000K. Four stars clearly show helium and hydrogen lines in their spectra. In the spectra of another three, helium, hydrogen, and metal lines can be detected. For these stars hydrogen and metal abundances were also determined by fitting appropriate model atmospheres containing these elements. Seven sample stars most likely have helium-rich atmospheres but do not show any helium lines. They either have featureless spectra or show calcium lines.