Background and Objectives: Nanostructured dispersed semiconductor structures are of some interest as functional materials for modern chemoresistive sensing and photocatalytic chemistry. Among the promising semiconductor materials for such applications is, in particular, titanium dioxide in the modification of anatase. Despite a significant number of experimental and theoretical works devoted to the consideration of electrophysical properties of anatase nanophase and various structures based on it, the features of degradation of electrical conductivity of such systems with time are not fully investigated. The aim of this work was to analyze the behavior of the fluctuation component of the voltage drop on partially conducting systems of interelectrode bridges made of anatase nanoparticles under conditions of direct current flow in the quasi-stationary regime (with a slow increase in the voltage drop) and as it approaches the threshold of flow, characterized by a rapid increase in the voltage drop. Materials and Methods: Experimental studies of the charge transfer fluctuations in disperse structures near the percolation threshold were carried out using specially prepared samples consisting of densely packed titanium oxide nanoparticles (TiO₂). The technique is based on the registration of time dependences of the voltage drop across the structures when a constant current flows through the system of anatase bridges. The behavior of fluctuation components during the measurement cycles was analyzed using moving estimates of the Hurst exponent of sample structural functions of intensity fluctuations. In addition to the sample values of the Hurst exponent, the sample normalized autocorrelation functions of the fluctuation component were calculated. To interpret the observed features, we propose a qualitative phenomenologicalmodel that considers the influence of random sequences of acts of blocking and soft breakdown of local conduction channels in the studied structures on the degradation of the effective ohmic conductivity of the structures. Results: It has been established that when approaching the threshold of percolation due to the depletion of the ensemble of free charge carriers (electrons) in bridges, there are qualitative changes in the dynamics of voltage drop fluctuations on bridge systems (in particular, a significant increase in the Hurst exponent of structural functions of voltage drop fluctuations, correlating with a sharp decline in the effective ohmic conductivity of the structures under study). “Soft” breakdowns of previously blocked local conduction channels may be due to the Poole – Frenkel effect, leading to the escape of trapped electrons into the conduction zone due to thermal fluctuations when the depth of traps decreases under the influence of an external electric field. Conclusion: The results obtained are of some interest from the point of view of further development of fundamental ideas about charge transfer mechanisms in dispersed semiconductor materials used in chemoresistive sensing and catalytic chemistry.