Transition metal silicides have gained considerable attention in the last decades as components in silicon-based microelectronics. Their favorable electrical properties together with a high thermal stability, as well as corrosion resistance against attack of oxidizing ambient, has made a number of them attractive for use in very-large-scale integration circuits as gates and interconnects and as reliable high-barrier Schottky or ohmic contacts of low contact resistance [1]. Recently, amorphous binary RexSi1-x thin films were prepared [2, 3]. Amorphous metalsemiconductor alloys represent a group of disordered materials with a length scale of disorder differing from that in heavily doped crystalline semiconductors. The Bohr radius of the deep levels in amorphous metalsemiconductor alloys is about one order of the magnitude smaller than that of shallow impurities in crystalline semiconductors. As a result, the critical concentration of impurities at the metal-insulator transition (MIT) was estimated to lie in the range of x between ~ 0.1 - 0.3, being about 103 times larger than in the crystalline materials [2, 3]. The low-temperature transport of amorphous RexSi1-x thin films has been studied in the metallic side of the MIT [4]. The purpose of this work is to investigate hopping conductivity in the insulating phase of the amorphous rhenium silicide thin films near the MIT. The amorphous RexSi1-x thin films have been prepared by co-sputtering from Re and Si targets in a cryopumped HV system onto unheated oxidized Si wafers. The film composition was varied in the range of 0.28 < x < 0.52 by changing the sputtering power ratio of the two targets. The film thickness was typically chosen between 60 nm and 150 nm. The film composition was determined by Rutherford backscattering and electron scattering microanalysis. The as-deposited films exhibit an amorphous structure. This was guaranteed by deposition onto unheated substrates. The amorphous structure was checked by electron diffraction and calculation of the radial density distribution function [2]. The electrical measurements were carried out using conventional dc techniques. Low-temperature conductivity of the amorphous RexSi1-x thin films with x = 0.285 – 0.351 is governed by a variable-range hopping (VRH) charge transfer, exhibiting the Mott [5] and the ShklovskiiEfros [6] VRH conductivity in different temperature intervals and preferably the three-dimensional regime of the hopping. Critical behavior of the characteristic VRH temperatures and of the Coulomb gap, Δ, pertinent to proximity to the metal-insulator transition at the critical value of xc ≈ 0.327, is observed. Analysis of the critical behavior of Δ yields directly the critical exponent of the dielectric permittivity, h = 2.1 ± 0.2, which is in agreement with the theoretical prediction [7]. On the other hand, values of the critical exponent of the correlation length, ν ~ 0.8 – 1.1 close to the expected value of unity [7] can be obtained from the analysis of the critical behavior of the VRH characteristic temperatures under an additional assumption of a strong underbarrier scattering of hopping charge carriers [8] in conditions, when the concentration of scattering centers exceeds considerably the concentration of sites involved in the hopping.