We present a general formulation of the existing theories of universal and non-universal behavior of the electrical properties in percolation systems. We then apply the theory to the three systems for which a non-universal behavior has been previously suggested. In particular, we derive explicitly a generalized non-universal behavior of the electrical resistivity and the electrical-resistance noise for the cases of two-component systems and for the case where the conduction takes place by tunneling. We emphasize the limits of the possible values of the corresponding critical exponents and compare them with existing experimental data. This comparison enables us to understand the many experimental data, which have been accumulated in the last two decades, on natural and artificial percolation-systems.