This article analyzes the priority directions of cooperation between the Russian Federation and the Republic of Kazakhstan in the field of space exploration. In particular, special attention is paid to the sharing of the unique complex “Baikonur”. Shown the leading role of Russia in the training of Kazakhstan's own space program. All these issues are discussed on the basis of normative-legal base of cooperation between the two countries in the field of use of cosmodrome “Baikonur”. Simultaneously analyzes the problems arising in the implementation of the Russian-Kazakh cooperation in space exploration which have practical importance for space exploration as the Russian Federation and the Republic of Kazakhstan. Particular attention is paid to the problem of ecological safety in the Republic of Kazakhstan related to the operation of the cosmodrome “Baikonur”. It is noted that Russia is responsible as the launching State, in accordance with the The Convention on International Liability for Damage Caused by Space Objects of 1972. Russian plans about the possible transfer of missile launches for new spaceports in the Russian territory, in particular to the launch site Vostochniy, to Plesetsk in Arkhangelsk region and to Kapustin Yar, Astrakhan Region are analyzed. The main proposals of the Kazakh side in this regard are also discussed.