We present magnetotransport measurements (up to 7 T) performed at very low temperatures (down to 20 mK) on a GaAs sample containing two parallel delta -doped layers whose carrier concentration can be varied by means of a gate electrode. With increasing negative gate voltage the resistance becomes more strongly temperature-dependent, indicating a more localized electron system. The magnetoresistance is found to be strongly anisotropic. When the field is parallel to the layers we find a large positive magnetoresistance which we attribute to orbital shrinking of the strongly localized donor wavefunction. In contrast, in the perpendicular orientation, we observe a strong negative magnetoresistance at low fields whose origin remains unclear, and the quantum Hall effect at larger fields. At low gate voltages both delta -layers are in the quantum Hall state whereas at larger negative voltages the layer adjacent to the gate becomes insulating. In the case of strong depletion the high-ohmic sample shows reproducible conductivity fluctuations as a function of either the gate voltage or the magnetic field. The fluctuations diminish at higher temperatures and larger measuring currents.