All around downtown Cairo, big white billboards have suddenly appeared explaining, in English, why the streets are torn up - A West German company is putting in new telephone cables.

Those Egyptians who can read the signs can be forgiven if they respond skeptically to this promise of better phone service. Over the years they have heard almost as many promises of improvement as they have busy signals and wrong numbers from a decaying, antiquated telephone system, one of the most maddening features of life in a maddening city.

"I tried to call you . . ." is the opening line of cocktail party conversations messages from people who cannot reach each other by phone. Some parts of the city can almost never be dailed from others.

Business executives fortunate enough to have telephone service say it is quicker and easier to communicate around the city by messenger than to waste time trying to phone. Government departments that need quick communications, like the military and the Suez Canal Authority, have their own telephone systems independent of the crumbling national network.

In all of Egypt, a nation of nearly 40 million people, there are only 375,000 telephones, according to a survey by the Continental Telephone Co. of Atlanta, which has a contract to prepare a master plan for telephone improvements here, Cairo, a city the size of New York, has 208,000 phones. The industrialized countries of the West have one telephone for every two people.

According to Arthur Taylor, continent's project director, adding more phones is not the answer,because the existing network is falling apart.

"It's just like the sewers and streets here," he said. "There are too many people and they just haven't fixed them up. It's like having a bunch of old cars and none of them run."

The mechanical deficiencies of the system, he said, are compounded by the "junk traffic" of people who dial again and again in their attempts to complete a call.

"Those calls don't go anywhere, and the equipment just grinds away," he said.

The government recognizes that Egypt is paying a high price in inefficiency, waste and lost business opportunities for the breakdown of the telephone system and has put a high priority on upgrading it. The man in charge is mahmoud Abdullah, chairman of the Telecommunications Authority, an affable man who is usually at his deak by 7 a.m. a rarity here.

He said in an interview that the phone system, some of which is more than 40 years old, suffers from "poor maintenance, overuse, junction bottle necks, a low budget, a shortage of spare parts for the old equipment, and the migration of technicians to other countries where they make more money."

He said there are more than 350,000 names on the waiting list for telephone service - almost as many as there are phones in the country - and that some of them have been waiting since the 1960s.

But, he said, "I think we are on the right track.Definitely by the end of 1978, you'll feel partial relief."

The new cables downtown, a U.S. built microwave relay system to be installed next year, new exchanges in Cairo and Alexandria and a coaxial cable to upper Egypt should mean "good service" by the end of 1979, he said. But he acknowledged that good service is a relative term.

International calls, for example, which now take 24 hours or more - partly because 380 of the 480 international ciruits are unused because of a lack of trained personnel to operate them - should be easier when direct dial service to Europe is installed by Ericsson of Sweden next year. Reliable telephone links to other Arab countries may be years away.

Abdullah said a call to Kuwait must be relayed to Alexandria and then by undersea cable to Beirut, where it is relayed again through Jordan and Iraq - a process that makes a call to Kuwait nearly impossible. Abdullah said the only prospect for improving that is a proposed Arab communciations satellite that Egypt, Saudi Arabia, Kuwait and the United Arab Emirates hope to put up in two or three years.

Taylor said the Continental survey, financed by U.S. aid, has "come to the conclusion that there is enough stuff here to give pretty good service if they'd just fix it. If you don't try to serve any new customers, just improve service to what you have, it could be done pretty quick."

others are less optimistic. Jamil Alaily, assistant manager of the Ericsson branch here, said, "in my opinion, with all these projects, service will improve a little bit within a year, but not much, because as service improves, more people will call, and that will create more demand."