Linda Stevenson's former husband, like many others across the country, had fallen years behind in his child-support payments when a new state law appeared to come to her rescue.

The law required her ex-husband's company to deduct $300 a month from his paycheck and send it to her.

The new procedure, increasingly popular in divorce cases, seemed to promise more financial security for Stevenson and her children Karen, 14, and Darren, 10.

Now that law and others like it across the country are drawing close attention from feminists charging subterfuge by the companies involved and from divorced fathers charging unfairness and overkill.

Stevenson's is a case in point.

The first support check deducted from her former husband's salary reached Stevenson in September.

Two weeks later she learned that he had been fired because of the wage deductions. Besides losing access to part of his $45,000 annual salary, she lost his company health insurance, which had covered the children.

"I was angry. I was very angry," said Stevenson, 37, an accountant who is trying to start a chocolate-confections business.

She has sued the company for $1 million. Her ex-husband has filed his own $4.8 million suit against his former employers.

But it will take at least a year for the cases to be heard, while the consequences of new child-support collection techniques reverberate nationwide.

A federal bill passed last year at the urging of women's groups gave states new authority to seize property, wages, dividends and tax refunds from parents who fail to make court-ordered child-support payments. The law allows wage deductions if the parent falls a month behind in payments.

James Cook, a Los Angeles-based administrator and lobbyist on child-support issues, said the bill reflected similar changes in state laws in California and elsewhere. Taxpayers, he said, have become outspoken about millions of dollars in welfare expenses for single mothers whose former spouses won't provide support.

According to the U.S. Census Bureau, 1.9 million of the 4 million single mothers entitled to child-support payments in 1981 received the full amount.

But some child-support experts, including representatives of a growing number of divorced-father organizations, argue that the new rules will only produce more difficult lawsuits like Linda Stevenson's.

"This is ridiculous," said David L. Levy, a Library of Congress copyright attorney who is president of the National Council for Children's Rights. "This is going to happen all the time. The employers don't want to be bothered with all this extra paper work."

Laws that allow sudden assignment of wages and property, sometimes with little or no notice, "take us well into the practices of a police state," said Vertner Vergon, president and founder of the Los Angeles-based Fathers of America.

Levy estimates that the new laws will take an additional $500 million a year in state and federal administrative costs. Fathers' groups such as his are asking that legislators strengthen laws guaranteeing visitation rights or providing joint custody as a fairer and cheaper way to ensure regular support payments. "Studies show that when both parents are involved, both parents are present and so are their wallets," Levy said.

To predictions that employers will make up excuses to fire parents who have troublesome wage assignments, Gloria Allred, president of the Women's Equal Rights Legal Defense and Education Fund and Linda Stevenson's attorney, replies that suits like Stevenson's will give teeth to the antidismissal provisions in new wage deduction laws.

Raymond A. Novell, attorney for Stevenson's former husband, John, said the 43-year-old safety executive and former highway patrolman is unemployed and must provide for his second wife and their children. He fell behind in support payments, Novell said, because he was ill and out of work for a year.

Watkins Motor Lines, the Florida-based transportation firm that fired John Stevenson, called him an "exemplary" employe and gave him regular raises, Novell said. Confident of his good standing, he told his attorney that wage assignment might be a convenient way to get the payments to his ex-wife. But soon after the assignment, Novell said, a Watkins personnel officer "called him in and waved the papers in front of him and said, 'We don't like these things. You'd better get it taken care of.' " The next thing he knew, he was fired.

A company spokesman would not comment on the case. The firm's official response to Linda Stevenson's suit says, "John Stevenson was terminated because of poor performance and not the wage assignment."

Novell said his client is still unemployed and has begun to despair of finding a job as good as the one he lost. Linda Stevenson said beyond the financial strain caused by more than $7,000 in missing support payments, her children are suffering from their father's absence. Child-support specialists say many fathers who fall behind in support payments stop visiting out of embarrassment.

Leaders of fathers' groups argue that the wage assignments are unfair because they target spouses with jobs and property.

But Allred says the new system provides necessary relief to single mothers. What is needed now, she said, is to "send a message to all employers" that the assignments are "for the protection of children," and that companies risk suit if they fail to comply.