Visionary labor leader Walter Reuther used to nag auto makers for a peek at the company books, challenging them to prove they couldn't pay the workers another nickel an hour. The companies always refused.

At Chrysler, under the new federal plan to bail that company out, those taboos are tumbling, opening for the United Auto Workers union a path to unprecedented influence over the nation's tenth largest industrial corporation. u

The new deal could also cause some headaches that Reuther never dreamed of.

Come spring, on the Detroit battlefields where the 1930s union organizers fought management goons, Chrysler will seat UAW president Douglas Fraser on its board of directors.

That alone is unique in the history of major American corporations.

But there's more.

In exchange for financial concessions from the union to aid its fight against bankruptcy, the company must give its employes, most of them UAW members, $162.5 million worth of Chrysler stock -- and the voting power that goes with it.

For UAW members, that will amount to about one-sixth of the company's stock, by union estimate. (about half of all the stock will be owned by employes, but that includes some white-collar workers, and substantial shares already owned by retirees, executives and others under existing stock purchase plans.)

Congress drew up the plan hastily, and many of the details still have to be figured out. Most of those affected, moreover, are still preoccupied with the basic question of whether the company will survive and haven't thought much, they say, about how it will actually work.

But the skeleton of the plan is this:

The company will, in effect, follow the government's time-honored strategy and crank up its printing presses, creating over the next four years at least $162.5 million worth of additional shares of stock. (One effect of that will be to water the value of outstanding shares.)

Starting in 1981, under what is called an Employe Stock Ownership Plan (ESOP), the stock will gradually build up in a trust.

The employes cannot sell their shares of stock until they leave the company or retire.

But each worker can direct the ESOP trustees how to vote his stock on a given question. The union and management still must resolve the question of how to vote the stock of employes who give no instructions.

"We've talked about the possibility that we might vote it in the same proportion as those for which instructions were received," said UAW official Howard Young.

If fraser could manage to vote the stock as a block, and if he found allies among the other directors on the 18-member board (some of them, like him, from outside the company), the speculation goes, he would have powerful leverage over company policy.

Fraser's new status as a "company man" gives the workers "a voice in the highest echelons" of the corporation, Fraser said after the arrangement was worked out with Chrysler chairman Lee Iacocca.

Others, however, contend that Fraser's new dual role will cause a severe identity crises, even for a man of his savvy and prestige among the workers. Wearing his two hats, he is liable, they say, the head himself off at the pass.

As a member of the board of directors, under law, Fraser's allegiance must be to the stockholders, to maximizing profit margins and dividends.

As a union leader, his duty is to the workers, to fight for the highest possible wages and benefits.

The two roles are so different mused Detroit financial analyst Arvid Jouppi, of John Muir & Co., that he envisioned a negotiating session in which Fraser would ask for something for the union. "Then he'd put on his board hat, and tell himself, 'You can't have it.' Back in his union hat, he'd say, 'Oh yes, I can.I've seen the books.'"

"It's a little like one of the new devices for scramblinb eggs without breaking the shell," Jouppi added, "deciding issues before they come up."

"I don't know how he's going to do it," said New York accounting specialist Neil A. Wassner, of Main Hurdman & Cranstoun.

What happens when Chrysler has to close some plants? Wassner queiried. Or what if, three years from now, it makes sense for Chrysler to make cars in Mexico, or some other country?

In each case, he said, as a union leader Fraser's natural role would be to oppose the move because it costs jobs for his members. That would be a "tremendous conflict" with his role as a director.

Not so, say union officials. "The fact that 125,000 shareholders will be UAW members will further strengthen Fraser's ability to fight for policies that are good from a worker's standpoint," said UAW spokesman Don Stillman. "This makes it more difficult than ever to argue there is a conflict."

A Chrysler official said the feeling among his management colleagues was that "probably it's more of a concern to the union than to the company" that Fraser will be sitting at the director's table. "It's a problem with their constituents."

The official recalled that when Chrysler was negotiating with a large battery of unions in Britain, the question of a labor seat on the board came up and "they opted not to take it. . . It's a tough problem."

As for the union's new access to company "secrets and policy making, he added, competitors such as General Motors have expressed more concern about that than Chrysler managers.

As one analyst put it, Chrysler in its scramble for rescue has had to reveal most of its secrets anyway and now "stands naked before the world."

For the moment, those most directly affected by the "Chrysis" indicated they are not focusing on the niceties of labor-management philosophy but on more basic questions: whether the company will survive, whether they'll have jobs next month, how much all this is costing them.

Congress approved $1.5 billion in federal loan guarantees to Chrysler -- the largest bailout in history -- last month on the condition, among other things that the 110,000 UAW workers give up $462.5 million out of their estimated $1.3 billion in raises over the next three years.

The stock issue was Congress' way of compensating the workers for those concessions.

The workers "could give a damn less about the philosophy," behind the new labor-management deal, said Michael J. Du Long, 36, a pipefitter for Chrysler and a UAW local committee-man. "They want the money in their pocket."

Du Long is one of the union representatives now circulating among the workers, explaining the painful realities of the new deal to them.

One of the things they were not pleased to learn, he said, is that they won't really possess their stock, can't sell it, until they leave the company, retire or die. "I got a lot of flak about that."

Most of the skilled tradesmen he had talked to that day told him they wanted to get hold of the stock immediately, he said, and sell it.

Others said they were pleased to get the stock.

As for the idea of putting Fraser on the board, union officials acknowledge that there was at first a good deal of concern about it among the rank and file.

Some workers wanted to know, for instance, if Fraser would be pocketing a fat corporate salary as director, and they wondered whether he would be "playing games" with the company, according to Vance Westley, who works at a Chrysler steel forging plant and is an officer in his UAW local. w

But Fraser has by all accounts quieted these anxieties. He and other UAW brass argue that his presence in the boardroom is only a modest step toward examples set by West Germany, Japan and Sweden which will give the union advance knowledge of, and a change to influence, any decisions affecting them, such as the traumatic closing recently of the company's historic Hamtramck plant, or potentially dangerous chemicals to be introduced into the workplace.

And Faser assured the members he would donate his corporate paycheck to the Walter Reuther Scholarship Fund.

"That rhetoric about a conflict of interest is a throwback to 1936," said Tony P. Jannette, 67, a Chrysler worker since 1928 and a UAW man since its first day of organizing. He has been president of local 51 for seven years.

"I think we've become sophisticated enough to know there are some ethics in the world," he said, and he added that he has too much faith in the union leadership to believe they would "sell out" just because they were sitting down with management.

What happens the next time the board sits down to plan its bargaining strategy against the union?

"Doug Fraser will walk out of the room, or not show up to begin with," said UAW spokesman Stillman.

Where collective bargaining is concerned, "we still have a healthy adversarial relationship" with all the auto companies, he said, and "we don't expect that to change."

As for those who assume that executives know more running the company than labor, he added, "For the last 10 year [at Chrysler] obviously they didn't . . . The union has been advocating the production of small cars since 1949. It fell on deaf ears."

Many analysts see the new Chrysler labor-management detente as a one-of-a-kind hybrid. While it may be a portent of the future, the way it was slung together represents nobody's ideal of how to cope with future crises.

"I'd be shocked if the union were to get representatives on the board of General Motors," said analyst Jouppi.

Indeed, recent examples are all in the opposite direction, Stillman said, citing union-bursting attempts by some companies, "hiring K-9 dogs and stringing up barbed wire," the rise of antiunion consultants, the business community's recent "holy war" against labor law revision.

Others, however, see it as a step on a new path. Hy Kornbluh, of the University of Michigan's Institute of Labor and Industrial Relations, said the significance of the Chrysler situation is in its "testing out of some new directions and new possibilities.

"It is part of the whole debate going on over changing the structure of corporate boards [bringing in] union representatives, consumer representatives . . . It's not irreverent anymore to raise the question."

The new Chrysler also represents the first foot in the door of a major corporation for proponents of the concept of employe stock ownership plans.

Sen. Russell B. Long (D-La.), a leading champion of ESOPs, by all accounts forced inclusions of that provision in the bailout legislation.

Case studies of successful ESOPs have shown that the greater the employe ownership, the greater their motivation, their productivity and, accordingly, company profits, said Jack Curtis, counsel to the Senate Finance Committee who rode herd on the legislation for Long.

"The senator sees it as a noninflationary way to stimulate productivity," Curtis said. (Union officials noted that productivity of employes had not been an issue in the Chrysler dilemma.)

Critics of ESOPs complain that some of the plans involve tax credits and therefore drain off general tax revenues, or that they break down natural, healthy labor-management antagonism, or that small businessmen oppose them because they don't want employ shareholders telling them what to do.

Some claim that ESOPs are as one congressional aide put it, "just a good way for management to palm off an ailing company on employes."

In any case, the government has been sponsoring the concept. Accounting specialist Wassner suggests that Chrysler would provide "a significant test case that SEOP proponents and detractors alike can watch closely" for evidence as to whether taxpayers are getting their money's worth.

Others contend that the Chryler plan is too much a hodge-podge to be a fair test of anything.

As the UAW's Stillman summed it up, "We don't argue that it's fair. We just argue that it's reality."