An experimental study of the longitudinal ρxx(B, T) and Hall ρxy (B, T) magnetoresistance as a function of the n-InGaAs/GaAs nanostructure transverse magnetic field, with single or double tightly-coupled quantum wells, depending on the width of the well, for magnetic field B = 0–12 T and temperature T = 0.05–100 K ranges, before and after low-temperature illumination by infrared radiation. Before illumination, a change in the samples' temperature dependence of zero-field resistivity ρ(T) was detected, from “dielectric” (dρ/dT < 0) to “metallic” (dρ/dT > 0). It is shown that the temperature dependence of resistivity is set by the mobility temperature dependence μ(T), the “dielectric” portion of which is related to the quantum corrections to conductivity in the diffusion and ballistic regimes, whereas the “metallic” portion is associated to the scattering of the carriers by acoustic and optic phonons. A slight change in the magnetic-field dependence of the longitudinal magnetoresistance ρxx(B, T) was observed with temperature, near the induction value corresponding to μB = 1. We also found unusual temperature dependence for conductivity components σxx(B, T) and σxy (B, T), at μB = 1. The σxx(B, T) curve has an observable temperature-independent point, whereas σxy (B, T) strongly depends on T at μB = 1. It is established that this regularity is caused by the nature of the temperature dependence of the charge carrier mobility μ(T), in both the diffusion and ballistic regimes. After IR illumination, positive persistent photoconductivity is observed in all samples, associated with a twofold increase in the charge carrier concentration. Resistivity in a zero-magnetic field ρ(T) for such samples also transitions from “dielectric” to “metallic” conductivity, at temperatures lower than before illumination. It is shown that the particularities of the transport after illumination are related to the manifestation of charge carrier concentration temperature dependence.