Six years ago, in what was heralded as a major innovation in U.S. labor-management relations, the United Steelworkers of America and the Big 10 steel companies signed an experimental agreement to stop nationwide strikes in their industry.

Now -- ironically just as the auto industry enjoys a respite from its habitual contract-time walkouts -- the steel industry's no-strike pact may be on its way out.

The early-warning signals come mostly from the company side of the bargaining table in the form of suggestions that the price tag for peace may be too high.

"I think the industry has to give a lot of consideration as to whether it [the no-strike agreement] has been worth the price -- and I say this as the man who committed them [the companies] to do it," said R. Heath Larry, who was the industry's chief negotiator when the pact was signed in 1973 and is the outgoing president of the National Association of Manufacturers.

Although bargaining for a new three-year contract won't begin for several months and the no-strike pledge will prevail for the 1980 contract talks, industry leaders confirm that just such a reappraisal is under way. And union leaders say the ball is largely in the companies' court.

"If they demand trade-offs that we consider unreasonable, that's the end of it," said USWA President Lloyd McBride, adding that he nevertheless would advocate a continuation of the pact "if it works well from our standpoint . . . and it has so far."

The so-called "experimental negotiation agreement" grew out of a mutual desire on the part of the union and the companies to stabilize the industry in the face of increasingly overpowering competition from abroad. A major problem was the boom-and-bust cycle of steel production at strike time, when plants worked at full tilt to build stockpiles before the strike deadline only to shut down and lay off workers after a new contract was signed.

New contracts were negotiated under the agreement in 1974 and 1977, with the two sides settling without recourse to the binding arbitration which the agreement prescribes as the alternative to strike action. Each no-strike pledge is prospective for three years, meaning the next contract must be negotiated under it. It also must be renewed by mutual assent in each contract. Hence scuttling of the agreement next year could mean a nationwide steel strike in 1983, but not in 1980.

As the price for going along with the no-strike pledge -- which is unique for a major industrial union -- the USWA insisted on certain minimum contract provisions, including wage increases of at least 3 percent a year, nearly full cost-of-living protection, a rich benefits package and a $150 bonus for each worker under the contract.

In an interview recently with Business Week magazine, U.S. Steel Corp. Chairman David M. Roderick suggested some of these provisions might be modified. For instance, he questioned whether the 3 percent annual wage boost continues to be justified in light of disappointing productivity increases in recent years. "I think it's time for an honest review to see what the benefits have been," he told Business Week.

However, the United Auto Workers recently negotiated a 3 percent annual increase with General Motors Corp., along with an even-more-generous cost-of-living formula in the third year of its contract and some other money gains that the USWA may want to pursue.

The USWA will be hard-pressed to accept a conspicuously thinner contract than the UAW, especially as the price of continuing the no-strike pledge, which is unpopular among a sizable number of steelworkers.

McBride said the no-strike pledge has helped the union keep abreast of inflation over the past six years, and "that's made it worthwhile."

But he insisted it won't be continued at the cost of an erosion of steelworkers' economic well-being, which already includes average hourly wages of nearly $11 for the 350,000 workers in basic steel -- near the top for all industrial workers.

Another problem from the companies' standpoint is that the negotiating agreement permits strikes at local plants over local issues, reducing the stabilizing effect of the industrywide agreement. a 4 1/2-month iron ore workers strike in 1977 stemmed in part from political infighting involving the industrywide no-strike pledge.

Beyond this are questions involving the long-range outlook for the import-plagued steel industry and the extent to which it will seek to boost productivity and cut labor costs in an attempt to survive in the worldwide steel market.

In an ironic commentary on the plight of the domestic steel industry and the union that has organized it, McBride noted that it is useless to look for clues to the 1980 steel bargaining in the United Auto Workers' recent strikeless settlement with General Motors because GM "makes several times more money than all the steel companies combined."