Transport coefficients (electrical and thermal conductivity, thermopower and Hall effect) of the monocrystals of approximants to the decagonal quasicrystals have been explored in the thesis. Because of the competition of the short range order and the periodic long range order, they have especially interesting physical properties, some of them resembling those of the decagonal quasicrystals. Decagonal quasicrystals possess two dimensional quasiperiodic arrangements, while in the third spatial direction these quasiperiodic planes are periodically stacked. It has been experimentally determined that the anisotropy of the physical properties of the decagonal quasicrystals depends on the number of the quasiperiodic layers along one periodic unit. The basic question here is whether the anisotropy of the physical properties between the in-plane and the stacking direction is the consequence of the quasiperiodic structural order within the 2D atomic layers versus the periodic order in the perpendicular direction or is it rather a conse-quence of complex local atomic order on the scale of near-neighbor atoms with no direct relationship to the quasiperiodicity. Due to the lack of translational periodicity within the quasiperiodic planes, quasicrystals are very complex systems for the theoretical analysis. The problem can be overcome by considering approximant phases to the decagonal phase. The structure of the approximants to the decagonal quasicrystals can be described by the pseudo decagonal atomic layers that correspond to the quasiperiodic layers in the decagonal quasicrystals, which are periodically stacked along the direction perpendicular to the layers. Local atomic order of the approximant phases is similar to that of the quasicrystals, but, since approximant phases are periodic solids in three dimensions; the theoretical simulations are straightforward to perform. The anisotropy of the transport coefficients of the decagonal quasicrystals measured along the stacking direction and in the quasiperiodic plane is decreasing with the increasing number of the decagonal layers in one periodic unit. It has been experimentally observed that in the approximants to the decagonal quasicrystals, which are 3D periodic solids, the amount of the transport coefficient anisotropy also decreases with the increasing number of the atomic layers that corre-spond to the decagonal layers in decagonal quasicrystals. It has been determined that the degree of structural perfection is also a factor influencing anisotropy amount.