The final statement by President Reagan and Soviet leader Mikhail Gorbachev said that the summit meetings ``were frank and useful. Serious differences remain on a number of critical issues. . . .'' The President and Gorbachev agreed to meet ``in the nearest future.'' Gorbachev will visit the United States and the President will visit the Soviet Union. The time and other arrangements remain to be made. The joint statement also said that the two leaders agreed on on a number of specific i ssues: Security: The two sides agreed to language frequently used by President Reagan in public addresses: ``that a nuclear war cannot be won and must never be fought.'' They stressed the importance of preventing any war between them, whether nuclear or conventional, and agreed they ``will not seek to achieve military superiority.'' Nuclear and Space Talks: Reagan and Gorbachev ``agreed to accelerate'' negotiations on nuclear and space arms in an effort ``to prevent an arms race in space and to terminate it on earth.'' Risk Reduction Centers: ``The sides agreed to study the question at the expert level of centers to reduce nuclear risk'' and hailed the modernization of the US-Soviet hotline. Nuclear Non-Proliferation: Both sides reaffirmed their commitment to the Treaty on the Non-Proliferation of Nuclear Weapons. Chemical Weapons: Gorbachev and Reagan ``reaffirmed that they are in favor of a general and complete prohibition of chemical weapons and the destruction of existing stockpiles of such weapons,'' and ``agreed to accelerate efforts to conclude an effective and verifiable international convention on this matter.'' Mutual and Balanced Force Reduction Talks: ``The two sides emphasized the importance they attach to the Vienna (MBFR) negotiations and expressed their willingness to work for positive results.'' Stockholm Conference on Confidence and Security Building Measures and Disarmament in Europe: Both leaders attached ``great importance'' to the talks and noted ``the progress made there.'' Process of Dialogue: Reagan and Gorbachev ``agreed on the need to . . . intensify dialogue at various levels,'' such as meetings of the leaders of the two countries, of their foreign ministers, and of the heads of other ministries and agencies. Northern Pacific Air Safety: The two leaders ``noted with satisfaction'' that a joint US-Soviet-Japanese agreement had been reached to promote safety on air routes in the North Pacific. Civil Aviation, Consulates: The two sides seek to reach a ``mutually beneficial agreement at an early date'' on resumption of air travel between the two nations. They agreed on the simultaneous opening of consulates in New York and Kiev. Environmental Protection: ``Both sides agreed to contribute to the preservation of the environment -- a global task -- through joint research and practical measures. In accordance with the existing US-Soviet agreement in this area, consultations will be held next year in Moscow and Washington on specific programs of cooperation.'' Exchange Initiatives: Reagan and Gorbachev agreed on ``the utility of broadening exchanges and contacts including some of their new forms in a number of scientific, educational, medical and sports fields'' and agreed to review resulting programs at their next meeting. (The foreign ministers of both countries signed a new cultural exchange agreement Thursday.) Fusion Research: ``The two leaders emphasized the potential importance of the work aimed at utilizing controlled thermonuclear fusion for peaceful purposes. . .''