There are three. All involve Trump’s effort to stop his longtime accounting firm and two banks from handing over his financial information to Democratic-led House committees and the Manhattan district attorney. The timing means the high court’s rulings will likely land this summer — in the heat of Trump’s reelection campaign.

Leading up to Tuesday’s arguments, Trump was on the losing side of a series of lower-court decisions. Judges in New York and Washington, D.C., rejected the president’s sweeping assertions of executive power and upheld the investigative powers of Congress and local prosecutors.

The high court now includes two Trump nominees, Justices Neil M. Gorsuch and Brett M. Kavanaugh. Listeners can expect to hear questions that draw comparisons to other major decisions on presidential power, rulings that went against Richard M. Nixon and Bill Clinton. In those cases, justices who had been put on the court by the two former presidents did not side with them.

Up first on Tuesday are the combined congressional cases — Trump v. Mazars and Trump v. Deutsche Bank. These cases involve attempts by three House committees to access the president’s business records from his accounting firm and financial institutions. Unlike past presidents, Trump has refused to make public his tax returns.

The House subpoenas followed testimony from Trump’s former fixer, attorney Michael Cohen, who alleged the Trump Organization exaggerated its assets to obtain better terms from its lenders and insurers. Two committees also subpoenaed Capital One and Deutsche Bank as part of their investigation into Russian money laundering and potential foreign influence involving Trump.

In the third case, Manhattan District Attorney Cyrus Vance Jr. is also seeking records from the Mazars firm. Vance has said he is investigating payoffs that Cohen testified he made to adult-film star Stormy Daniels and former Playboy model Karen McDougal before the 2016 election. Both women have alleged having affairs with Trump years ago, claims the president denies.

Cohen has already pleaded guilty to a federal charge related to those payoffs, but Vance’s office says it wants to know if any state laws were also broken.

Because the justices are not together and can’t see each other, they have abandoned their usual free-for-all approach to oral arguments. Instead, each justice is afforded time to ask questions, and each has taken advantage.

Justice Clarence Thomas, for instance, has asked questions at all six of the teleconferenced arguments. He once went for a decade under the old system without asking a question.

Chief Justice John G. Roberts Jr. is much more active in his new role, shutting down advocates — and very rarely, a justice — when they get too wordy. Some have been surprised at how abruptly Roberts has cut off an advocate, but he is trying to make the train run on time.

Still, the new form takes longer: The two arguments Monday were scheduled for a combined two hours, and yet the sessions stretched for three hours, fifteen minutes.

The format goes like this: The advocate for the losing party in the lower courts goes first and has two minutes of uninterrupted time. Roberts then questions the lawyer, and the order for the rest of the questioning follows seniority: Thomas, Ruth Bader Ginsburg, Stephen G. Breyer, Samuel A. Alito Jr., Sonia Sotomayor, Elena Kagan, Gorsuch and Kavanaugh.

So far, only Breyer has passed up the chance to question a lawyer, and only once. The process is repeated for the other side. Then the initial lawyer has a few minutes for rebuttal.

The first lawyer up will be Patrick Strawbridge of Boston, a member of Trump’s team of private lawyers who have argued the congressional subpoenas are politically motivated, unprecedented attacks on the presidency.

Also arguing on Trump’s behalf will be Deputy Solicitor General Jeffrey B. Wall.

House lawyers have warned that Trump’s broad claims of absolute immunity, if upheld by the court, would upend the Constitution’s system of checks and balances and essentially put Trump above the law.

After Letter, Strawbridge will have a few moments for rebuttal.

In Trump v. Vance, the president’s private lawyer Jay Sekulow of Washington will go first. Sekulow was Trump’s lead private attorney during the Senate impeachment trial that ended with Trump’s acquittal in February.

When they are finished, Roberts will call on Carey R. Dunne, general counsel for Vance. Then Sekulow will have time for rebuttal.