Several compositions of quaternary materials in the As-S-Ge-Te system were synthesized by meltquenching technique and the respective thin films have been fabricated. Shown by AFM, SEM and X –ray analysis the nature of the films was predominantly amorphous. In order to elucidate the mechanisms of charge transport   in these films, the DC  and AC conductivities  have been carried out in the 10 -200  0C temperature range and 5 – 107 Hz respectively.  Direct current - voltage characteristics were measured at different temperatures in normal air ambient conditions, using a priory established electrically transparent (ohmic)  Ag  contacts. Applying these data, the temperature dependence of DC conductivity has been highlighted. Being presented as lnσ versus   103/ T  it  consists of two straight lines with different slopes, which gives evidence that the charge transport occurs by different mechanisms, ether  via non localized  (extended ) states above mobility edges or by phonon  assisted hopping via  tails of localized states, close to mobility edges.   Respectively, the entire conductivity in mentioned above temperature range can be expressed as: exp()exp( 2 2 1 1 kT E C kT E Choppext exp(min1 k C (2) where min is the minimum metallic conductivity, that is the conductivity by charge transport exactly on the mobility edge;  - is the temperature coefficient of gap edge broadening, which is approximately  a half of temperature coefficient of the optical gap. Following the Mott and Davis model of de density of states in disordered materials [1] the minimum metallic conductivity and the mobility gap of glassy materials in question have been estimated. At temperatures lower than  80 0C  (at list up to  10 0C ) the  electrical  conductivity  is released  by phonon  assisted hopping via  tails of localized states, close to mobility edges. The AC conductivity has been found to depend on frequency as:   n A  (3)   with 7 ,0n and A  a constant.   In the 103 – 106  Hz frequency range, the AC  conductivity was observed to be temperature dependent, while in the higher  frequency region it  appeared to be nearly independent on temperature. It is assumed [2] that in the frequency range until 3 kHz the AC conductivity is due to charge hopping between tail localized states.  AC is higher than DC conductivity:  at 3 kHz and room temperature their ratio being of 3 . This ratio, increases further at frequencies higher than 3 kHz, but itself   becomes  less and less temperature dependent, along with  a stronger   frequency  dependence. Such behavior is interpretable in terms of transition to a mechanism of hopping that includes the states N(EF)   in the middle of the mobility gap. Using the theoretical formula derived by Austin and Mott for such a conductivity [3], the composition dependent density of states N (EF) has been estimated.  For  As2Te13Ge8S3  it appears to be  in the range of  . 103,1)( 3 121  cm eVEN F