It is known that all candidates in dark matter (DM) particles (neutrinos, axions, supersymmetric particles etc.) can not explain the basic properties of DM. The same can be said on the proposed candidates in dark energy (DE) (for example, quintessence). In the paper it is shown that some problems connected with DM and DE can be solved in the framework of the byuon theory. Basic axioms and some conclusions of this theory are discussed. The existence of fundamental unobserved elements in nature, byuons is declared. Physical space in our Universe is the quantum medium of special objects 4b, formed in four-contact interactions of byuons (m4b c2 ≈ 33eV). These objects determine the average density of substance (DM) in the Universe ~10-29 g cm-3. The byuon theory predicts a new interaction of natural objects with physical vacuum. This new force can cause the observed acceleration of our Universe. The estimations show that it is higher than the gravitational force at distances of order to 1026-1028 cm. Some other consequences of the byuon theory are considered