Abstract. In framework of the 2D - dissipative tunneling theory in approximation of a rarefied gas of the «instanton - antiinstanton pairs» at a finite temperature under the conditions of an external electric field, the features of tunneling transport for planar structures with quantum dots (QDs) from colloidal gold, that have metamaterial properties, have been studied. It was experimentally shown that, depending on the positioning of the cantilever needle of a combined atomic force and scanning tunneling microscope (AFM / STM), either above a single quantum dot or between two neighboring quantum dots, either a single or double effect of 2D tunneling bifurcations have been observed, respectively. It is such a double bifurcation regime, as our theoretical model has shown, that is associated with the manifestation of the metamaterial properties by the structure under study. A convincing qualitative agreement between the experimental I – V characteristics and the field dependence of the 2D - dissipative tunneling probability in the two studied modes, taking into account the observed quantum beats in the vicinity of the 2D bifurcation points, has been obtained.