As Bell System executives like to say, the telephone and computer have been living together so long, they ought to get married.

That marriage is being arranged now, at the Federal Communications Commission, in the House communications subcommittee and in the Senate -- where a major breakthrough took place late yesterday, in the form of a compromise legislation supported by influential Democrats and Republicans.

The telephone and computer union that may result from these deliberations is expected to revolutionize the way businesses and households communicate with one another. In addition, it is possible that broad legislation dealing not only with the tele-communications business but also with broadcasting may emerge. The Senate bill offered last night, for example, encompasses all of these communications fields.

But holding up the ceremony is a fundamental question concerning the future of the telecommunications market: What to do about American Telephone & Telegraph Co., its nearly $100 billion in assets, its revenues of $36 billion a year, and its $1 billion annual research budget?

The Bell System is yearning to leap into the market for telecommunications equipment. It is conducting an experiment with a dozen Albany, N.Y., subscribers, permitting them to call up telephone numbers from both the white and Yellow Pages on a small telescreen next to a phone. The number on the screen can be dialed automatically by pressing a single button.

Another experiment permits about 160 households in Coral Gables, Fla., to summon information from newspaper and magazine files, check airline flight schedules, order home-delivered meals, scan the advertisments of 31 subscribers, and study Spanish. Southern Bell, an ATT subsidiary, provides the equipment and the transmission services for Viewdata Corp. of America, the sponsor.

ATT cannot take the full step, however, until the FCC and Congress alter a 1956 consent decree between ATT and the Justice Department that bars the company from the sale of data processing services.

"If the constraints on our range of services are removed, we will be ready to take full advantage of the new competitive freedom," ATT vice chairman William S. Cashel Jr., said recently.

The FCC's answer in an April 7 ruling requiring ATT and its major communications competitor, General Telephone and Electronics, to sell new, "enhanced" communications services through a separate subsidiary.

ATT has indicated it will appeal the FCC's move to separate the company into a regulated, basic telephone company, and an unregulated subsidiary selling telecommunications services.

The FCC's decision is also opposed by many of smaller companies already in the field, who fear the power of ATT's telephone monopoly, generated by its millions of subscribers, will spill over into the unregulated market, giving it unbeatable muscle there.

To critics such as the Computer Communications Industry Association (CCIA), the FCC has strayed far beyond its authority in rewriting the Justice Department's 1956 consent agreement with ATT, which ended an antitrust investigation of the Bell System. The Justice department, which has a current antitrust suit against ATT, has that responsibility, the CCIA contends.

The FCC invited Congress to uphold its April ruling by enacting new legislation to charter the course of the telecommunictions industry.

That attempt got underway again yesterday, before the communications subcommittee of the House Commerce Committee, headed by Rep. Lionel Van Deerlin (D-Calif.).

Van Deerlin's bill, which has appeared in several forms in its long path through the subcommittee, also separates ATT into a regulated, basic telephone company, and an unregulated subsidiary free to fight and business equipping offices and homes with telecommunications services.

ATT's competitors have little confidence that either the FCC ruling or the Van Deerlin bill could prevent ATT from using research paid for by its telephone subscribers to develop products for its unregulated, competitive subsidiary, if it chose to.

The Van Deerlin bill generally requires ATT to shift "applied" research on new products to its unregulated subsidiary over a five-year period, with longer periods of research on components and sub-components. ATT says it can adjust to that plan. Its opponents worry how to thin-staffed FCC could regulate such fine distinctions between basic and applied research.

Neither the FCC or the House subcommittee is likely to settle the debate soon.

The Senate compromise, formally introduced last night, would accomplish many of the goals in FCC decisions and the House bill. Backed by Senate communications subcommittee chairman Ernest Hollings (D-S.C.), Commerce Committee Chairman Howard Cannon (D-Nev.) and ranking committee Republicans Bob Packwood (Ore.) and Barry Goldwater (Ariz.), the compromise is scheduled for markup on July 24.

Substantial deregulation of the telecommunications business and broadcasting is at the heart of the new Senate bill. All communications firms except the largest telephone carriers would be fully freed from regulation, while the big telephone firms, including the Bell System, could set up separate subsidiaries (same owners but different directors, employs and research) to compete in the deregulated businesses.

Basic telephone service would continue under FCC regulation, under the congressional proposals.