A race is on to put the first privately owned communications satellites into orbit above Japan. Triggered by the Tokyo government's recent far-reaching decision to end its state-owned monopoly of the telecommunications industry, it seems sure to bring hundreds of millions of dollars in orders for U.S. satellite makers.

Hughes Communications Inc. and Ford Aerospace Communications Corp. are set to build finished satellites for two newly licensed and competing Japanese companies, with service to start in 1988. A third Japanese company linked to RCA Corp. is seeking government permission but may not get it.

Distribution of video programming by Japanese television networks probably will be the most important use. The satellites also could handle high-speed data transmission, cable TV, private video conferencing, newspaper facsimiles and ordinary phone conversations.

Officials here hope they will help Japan catch up with the United States in telecommunications services, which they feel had fallen behind under the old system, a monopoly under the mammoth state-owned Nippon Telegraph & Telephone Public Corp. (NTT).

About 25 different communications satellites are already in service in the domestic U.S. market. In contrast, Japan, which until this spring banned the purchase of finished satellites from abroad, has only two communications satellites and one mostly crippled broadcast satellite in operation.

Compared with NTT's $20 billion in annual sales, the new companies will be small. "We are not aiming at a big part of NTT," said Kenichi Itoh of Space Communications Corp., one of the satellite companies. "We should say we will be a fly stuck on an elephant."

On April 1, new laws came into effect stripping NTT of its monopoly and making it a private corporation, though for the present all of its shares remain in government hands. The telecommunications services field was formally opened to competition, though considerable government regulation remains.

In June, the Japanese government approved applications from Space Communications and another newly formed company, Japan Communications Satellite Co. (JCSAT), to operate satellites. International frequency allocations, other Japanese permits and financing remain to be secured, but both companies say they are certain to go forward.

JCSAT is a joint venture between two of Japan's largest trading houses, C. Itoh & Co. (it has a 40 percent share) and Mitsui & Co. (30 percent), and Hughes Communications, which has 30 percent. Last month, the company paid Hughes the first installment for what is to be a $300 million system composed of two satellites and two ground stations.

Each satellite will have 32 transponders, the basic unit of operation in communications satellites, with each transponder capable of handling one high-quality video channel or 2,500 voice circuits.

Hughes has begun design work and parts procurement for the satellites. The first is scheduled to be launched in December 1987 and enter service in February the following year. Number two will go aloft in April 1988 and start service in June.

Space Communications is a venture between the Mitsubishi Corp. and the Mitsubishi Electric Corp. Ford Aerospace is to build a pair of satellites but has taken no equity position in the company. It is talking of a February 1988 launch, with service two months later.

The cost of the two satellites, each of which will have 35 transponders, plus launch and insurance, will be about $265 million, according to Itoh.

Communications satellites, launched into "geosynchronous orbits" that keep them over a fixed point on the earth's surface, serve as relay stations. They receive signals sent from the ground, amplify them and send them back down to be picked up at different points.

Satellites are often said to be best applied in large countries such as the United States or Indonesia, where the cost of land lines is high. But the companies contend they will be ideal for linking small Japanese communities and remote islands and allowing cheaper "point-to-multipoint" transmissions.

Japanese TV networks currently do most of their program distribution over land lines leased from NTT. Satellite companies contend they will be able to offer a lower price and greater simplicity, with many stations receiving simultaneously.

An added advantage of satellites for Japan is their invulnerability to the country's frequent earthquakes, which can cut land lines and necessitate costly repairs.

In data transmission and telephone calls, they will be competing with NTT and three more newcomers, which since April 1 have been licensed to build ground-based or "terrestrial" microwave and optical fiber systems along the Tokyo-Osaka corridor, the heart of industrial Japan.

Here satellites' broad sweep is cited. "Terrestrial people can cover only from Tokyo to Osaka. We can cover all of Japan," says Itoh. The flip side of that argument is that the really big business is between those two cities.

The licensed companies say there is business enough for two, but not a third. "Perhaps after several years," muses JCSAT President Hiroshi Kamiya. Itoh says he is actively lobbying against any further expansion of the field.

The Ministry of Posts and Telecommunications still is studying an application from a third hopeful entrant, a venture led by Sony Corp. and the trading House Marubeni Corp., with satellites to come from RCA. But as one ministry document notes, there is fear that a third company would mean all would be "ruined together."

The two approved projects have satisfied in part long-standing U.S. government efforts to force Japan to open its market for satellites. Sales had been hampered by Japanese policy that government-owned satellites be built by the fledgling local industry, to give it experience in this crucial field, even if cost is higher and product quality lower.

Equipment the new companies will get is far beyond what Japan could produce.

The two government-owned satellites that NTT now uses were built by Mitsubishi in conjunction with Ford Aerospace. A pair of more advanced models is now under development, for launch in 1988.

Official Japanese policy is now that future government satellite procurements will be open to foreign bidders, as long as it does not interfere with domestic development programs. U.S. officials have been pressing unsuccessfully for almost 18 months for clarification of what that means.

Meanwhile, the two companies are pressing ahead with marketing services that still are widely unknown in Japan. JCSAT claims to have obtained letters of intent from 37 companies for services that would tie up almost all of its capacity. It concedes that they are not firm commitments, however.