  The CRESST experiment monitors 300g CaWO_4 crystals as targets for particle
interactions in an ultra low background environment. In this paper, we analyze
the background spectra that are recorded by three detectors over many weeks of
data taking. Understanding these spectra is mandatory if one wants to further
reduce the background level, and allows us to cross-check the calibration of
the detectors. We identify a variety of sources, such as intrinsic
contaminations due to primordial radioisotopes and cosmogenic activation of the
target material. In particular, we detect a 3.6keV X-ray line from the decay of
41-Ca with an activity of (26\pm4)\mu Bq, corresponding to a ratio
41-Ca/40-Ca=(2.2\pm0.3)\times10^{-16}.
