The noise in current biased aluminium single electron tunneling (SET) transistors has been investigated in the frequency range of 5 mHz <f <30 Hz. A refined high frequency (HF) shielding including resistive coaxial lines, that prevents spurious electromagnetic radiation and especially high energy photons emitted by the 4.2 K environment from reaching the sample, allows us to study a given background charge configuration for many hours below [approximate] 100 mK. The noise at relatively high frequencies originates from internal (presumably thermal equilibrium) charge fluctuations. For f >= 10 Hz, we find the same input charge noise, typically QN = 5 × 10–4 e/Hz1/2 at 10 Hz, with and without the HF shielding. At lower frequencies, the noise is due to charge trapping, and the voltage noise pattern superimposed on the V(Vg) curve (voltage across transistor versus gate voltage) strongly depends on the background charge configuration resulting from the cooling sequence and eventual radio frequency (rf) irradiation. The measured noise spectra which show both 1/f and 1/f1/2 dependencies and saturation for f <100 mHz can be fitted by two-level fluctuators with Debye–Lorentzian spectra and relaxation times of order seconds. In some cases, the positive and negative slopes of the V(Vg) curve have different overlaid noise patterns. For fixed bias on both slopes, we measure the same noise spectrum, and believe that the asymmetric noise is due to dynamic charge trapping near or inside one of the junctions induced when ramping the junction voltage. Dynamic trapping may limit the high frequency applications of the SET transistor. Also reported on are the effects of rf irradiation and the dependence of the SET transistor noise on bias voltage. ©1998 American Institute of Physics.