Problems of implementation of state jurisdiction in the sphere of space are of great relevance and importance nowadays and they are primarily caused by the issue of multinational activity in space. Many scientific achievements in the field of an outer space exploration have become possible due to the teamwork of researchers from different countries. This teamwork includes joint projects of launching artificial satellites, delivering spacecrafts with international crews on board to the orbit, creating the International space station, and the long-term joint development and use of resources of celestial bodies, including the Moon and planets of the Solar system. In these circumstances, some problems related to the state jurisdiction cannot be overlooked.The article analyzes universal conventions concerning the issue of activity in space as well as multilateral agreements involving a limited number of participants, bilateral agreements regarding cooperation in the field of exploration and use of outer space for peaceful purposes and the UN General Assembly Resolution. The questions concerning the International space station and the cosmodrome Baikonur jurisdiction, the prospects of development and use of resources of celestial bodies, particularly those of the Moon, are considered separately. The problem of delimitation of the space and airspace for practical implementation of jurisdiction of the states is also designated.In the conclusion it is substantiated that the principles of criminal jurisdiction are applicable today to the space activity of the states.