We analyse the charge transport mechanism in semi-insulating (SI) materials for N-SI-N and P-SI-P structures. The SI layers are large band gap semiconductors obtained by deep levels compensation of residual shallow donors or acceptors. A preceding theory is extended to the case of two, donor or acceptor, deep compensating levels [1]. The conduction mechanism is complex: ambipolar transport, heavy recombination, space charge effect and we show that the current is controlled by both bulk and interface effects at the reverse biased N-SI or P-SI junction. We develop a simple model, without the usual assumption of space charge neutrality, valid up to the beginning of one carrier space charge current. We show that a linear relation exists between the bulk excess free carrier densities and that depending on the value of a quantity M, given as a function of the deep levels electrical parameters, energy position, concentration and capture cross sections, as well as the dopants concentrations, the conduction mechanism is either contact controlled showing a pronounced current saturation effect or bulk controlled with one and for long sample, two, quasi linear J-V-alpha relationship. Numerical modelisations of the drift-diffusion transport model confirm these analytical results for the case of one or two compensating deep levels. GaAs (SI) or InP (SI) layers are used for their high resistivity and insulating properties in FET technology, in buried heterostructures, diode laser and in radiation detectors technologies. These results are of importance for the interpretation of conductivity and Hall Effect measurements and explain the parasitic side-gating effect in GaAs or InP MESFET's. (C) 2012 Elsevier Ltd. All rights reserved.