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Low-level gamma-ray spectrometry with large volume HPGe detectors has been widely used in analysis of environmental radionuclides. The reasons are excellent energy resolution and high efficiency that permits selective and non-destructive analyses of several radionuclides in composite samples. Although the most effective way of increasing the sensitivity of a gamma-ray spectrometer is to increase counting efficiency and the amount of the sample, very often the only possible way is to decrease the detector's background. The typical background components of a low-level HPGe detector, not situated deep underground, are cosmic radiation (cosmic muons, neutrons and activation products), radioactivity of construction materials, radon and its progenies. A review of Monte Carlo simulations of background components of HPGe detectors, and their characteristics in coincidence and anti-Compton mode of operation are presented and discussed.