The Supreme Court will decide whether federal agencies should stop getting such a strong voice when interpreting their own regulations, in a case that could significantly influence how judges decide challenges to environmental, health care, immigration, veterans benefits and other rules.

The justices on Monday agreed to hear arguments about overturning two Supreme Court rulings at the heart of administrative law, Bowles v. Seminole Rock & Sand Co. in 1945 and Auer v. Robbins in 1997. In the case, the court could accomplish part of what some conservative members of Congress have sought to do legislatively.

Under those old rulings, federal judges give deference to the views of agencies when one of its regulations is ambiguous. But the decisions have faced growing criticism in conservative legal circles and from the justices themselves as giving too much power to the executive branch.

“Auer deference may not be long for this world,” University of Michigan law professor Nicholas Bagley tweeted about the court’s announcement.

Chief Justice John G. Roberts Jr. and Justice Samuel A. Alito Jr., two of the five conservatives on the court, wrote in a 2014 case that it may be appropriate to reconsider the deference to federal agencies in a future case. And in the same case, the late Justice Antonin Scalia called Auer deference “a dangerous permission slip for the arrogation of power.”

It’s not immediately clear whether the Supreme Court, where conservatives hold a 5-4 advantage, would overturn the rulings or what would replace them. But legal experts believe the newest justices, Neil M. Gorsuch and Brett M. Kavanaugh, generally have concerns about the power of federal agencies.

The same concerns have been echoed in Congress. Texas Rep. John Ratcliffe, a member of the House Judiciary Committee, introduced a bill along with more than 50 other Republicans that would modify the scope of review for agency actions that would not give deference to the agency’s interpretation. And Utah GOP Sen. Orrin G. Hatch, a member of the Senate Judiciary Committee, introduced similar legislation in the Senate.

Hatch wrote in a 2016 online symposium that the growth of the administrative state, in part because of the Auer doctrine, “has diminished Congress’s ability to check agency actions that stretch statutory authority beyond the breaking point.”

Ratcliffe, Hatch and other Republicans also express concern about the fallout of the more well-known administrative law doctrine that comes from the Supreme Court’s 1984 decision in Chevron U.S.A. v. Natural Resources Defense Council Inc. The Chevron doctrine, in which judges give deference to agency interpretations of statutes it administers, is not at issue in the current case before the Supreme Court.

In the current case, a Marine who served in the Vietnam War challenged a VA decision about service-connected disability benefits for post-traumatic stress disorder, and whether some new documents are “relevant” to the decision.

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