The major difficulties in a hydrogen-oxygen fuel cell with a solid polymer electrolyte [1][2][3][4][5] emerge when it is attempted to ensure optimum operation of the cathode, i.e. the oxygen electrode. We will explore the same model of the active layer of a porous electrode as in [6]. Specifically, we will assume that the active layer may comprise a mixture of four constituents. The first, the substrate grains, consists of agglomerates of carbon particles, which provide for electron conduction. The second constituent is microparticles of platinum (catalyst) embedded into these agglomerates. The third constituent is particles of a hydrophobizing agent (polytetrafluoroethylene), which play the role of a binding agent and which can facilitate creation of hydrophobic pores in the active layer. At present the active mass of the cathode is prepared both with use of polytetrafluoroethylene and without it. And finally the fourth constituent is the grains of a solid polymer electrolyte (Nafion), which ensure ionic conduction.We will embark now on the description of the adopted computer model. For the porous electrode we will select a cube of conditional dimensions N s × N s × N s = . It is desirable to have a model of a macroscopic size. What this means is that the following condition must be fulfilled: N s should amount to a few tens of elements of structure; in what follows we will always assume that N s = 100. Let us explore a cubic lattice of points. Every point is a cube randomly filled either by a solid electrolyte or by a substrate with platinum particles embedded into it, or this is an empty space. Further on, to simplify analysis, we will assume as we did in [6] that concentrations of points filled with electrolyte and substrate are identical and denote their bulk concentration as g . This is a major parameter of the system under consideration. It is obvious that 0 ≤ g ≤ 0.5 (no poresvoids are present in the electrode at g = 0.5). The length of the edge of one cube (all cubes are identical geometrically) will be denoted with L . One more parameter of structure is the average degree of filling of the substrate grains by platinum, denoted by g Pt (0 ≤ g Pt ≤ 1) . The platinum concentration in a randomly selected substrate grain can assume any value; however, when averaged over all the substrate grains, it needs must be equal to g Pt .In [6] we discussed at length how the electron and ion clusters emerge in the model under investigation at N s 3 Abstract -A computer model of the active layer of the cathode of a hydrogen-oxygen fuel cell with a solid polymer electrolyte is studied. The active mass of the electrode consists of equidimensional grains of the substrate (agglomerates of carbon particles with platinum particles embedded in them) and a solid polymer electrolyte (Nafion). The flooding by water can be experienced by both the pores in the substrate grains, which facilitate the oxygen penetration into the active layer of the electrode, and the voids between the grains. All possible versions of the flooding of t...