A new physical model of relative permittivity and derived quantities of fractal structures, contrary to the current concept, predicts their dependence on the fractal dimension (D) and on the extent (R) of the considered structure. The scaling of considered quantities predicted by our theory is similar toR(D-d), where d is dimension of Euclidean space. Hence, fractality, a feature often found in physical, chemical, and biological systems, influences also basic properties of such systems that, so far, were believed to be material and not structure related, The theory has been experimentally verified by electrochemical measurements of capacitance of adsorbed layers of nonionic surfactant Triton-X-100 and linoleic acid that have fractal structure. The experimental results, substantiating theoretical predictions, are presented, and the influence of relevant parameters is discussed.