Climate change has far-reaching adverse consequences on eco-systems, human lives and health as well as on economic progress, so the question arises whether the state is resposible for climate change and its adverse effects or whether relevant international documents dealing with climate change (UN Framework Convention on Climate Change, Kyoto Protocol and Paris Agreement) should prescribe and define responsibility of a state (or more states) for climate change and its adverse effects which occur due to non-compliance with obligations assumed by the above-mentioned international documents. In the climate change context the primary obligation of the state is to reduce its greenhouse gass emission and thus to protect the atmosphere as the common good of all mankind. Recently increasing attention has been paid to adaptation to the adverse effects of climate change and to obligations of developed countries to assist the least developed countries and developing countries, which are at the same time the most vulnerable to the adverse effects of the climate change, when financing and implementing adaptation measures. The paper also analyzes the grounds and elements of general international liability of states for wrongful acts, as well as international customary rules - no-harm rule and due diligence standard of a country's behavior, as sources of the international resposibility of countries that violate these customary legal rules.