FRANKFURT, Germany — The U.S. is looking for multibillion dollar penalties from Germany’s biggest bank and its biggest carmaker. The European Union is demanding similarly large sums from America’s most valuable tech company, Apple.

Both sides of the Atlantic appear to have become emboldened to crack down on big companies that are found to have misbehaved. Some analysts say it’s a sign that governments, several of which have elections looming, are feeling political pressure to act against corporate wrongdoers.

But the crisscrossing crackdowns have also frayed nerves, especially in Germany, and led to dark talk about a tit-for-tat war in which the U.S. and EU target each other’s companies to gain trade advantage.

In particular, the penalty of as much as $14 billion hanging over Deutsche Bank, Germany’s only bank of global significance, has put the German political and business elite on edge.

“What we are going through are moves that are similar to a trade war,” said Peter Ramsauer, the chair of the German parliament’s economy committee.

“In the U.S. there is a long tradition of using every occasion for conflict similar to a trade war, when it serves their own economic interests,” Ramsauer was quoted as saying by the Die Welt newspaper. “Connected with that are the extortionate demands for compensation, as we see in the Deutsche Bank case.”

Deutsche Bank is among a group of banks that the U.S. government says sold dodgy mortgage-based bonds that helped trigger the 2007-8 financial crisis. But there are concerns that if the penalty is too big, the bank may have to raise new capital from investors or even need a government bailout. Chancellor Angela Merkel may be reluctant to approve such aid, which would also be a severe political embarrassment ahead of 2017 national elections.

News of the potential fine on the bank followed by days a decision by the EU Commission’s demand that Apple repay $14.5 billion in what were ruled improper tax benefits from Ireland. That preceded a U.S. court deal to have Volkswagen pay $15 billion over its cars that cheated on diesel emissions tests. Volkswagen is in talks with the Justice Department that could lead to another financial penalty.

The Apple case seems to have irked the U.S. authorities in part because the back tax that the tech company has to pay to Ireland would detract from a huge sum of money — about $200 billion — that Apple keeps outside the U.S. and would be subject to U.S. taxation when repatriated. Apple and the Irish government are appealing.

German finance ministry spokeswoman Friederike von Tiesenhausen, asked whether the large proposed fine against Deutsche Bank was retaliation for Apple, said, “I don’t share that assessment.” She added, however, that “the German government assumes that a fair result will be reached at the end of this process as well, on the basis of equal treatment” like that afforded U.S. banks.

U.S. Justice Department officials declined to comment, as did those at the European Commission. EU Competition Commissioner Margrethe Vestager, who ruled against Apple, said that “I am absolutely certain that the decision on Deutsche Bank is built on the facts of the case and American legislation.”

Guntram Wolff, head of the Bruegel think tank in Brussels and a former official at Germany’s central bank, the Bundesbank, dismisses the tit-for-tat idea.

“I think it’s one of those perfect theories that, unless you are actually in the minds of the people who did this, who took the decisions, is impossible to approve or disprove,” he said. “So it’s close to what I would call, can I say, conspiracy theories — it’s impossible to prove, but it’s also impossible to contradict it.”

He said it’s much more likely that policy makers on both sides want to be seen as being tough on companies that are found to misbehave.

“The elites are under pressure and the citizens are demanding change, and they demand it in a sort of indiscriminate way,” he said. “I think there is a perception among policy makers that it is related to issues of fairness, to issues of equity, to issues of perception, that the small guy pays, the big guy doesn’t pay.”

U.S. officials have been seeking fines and compensation from big banks — not just Deutsche Bank — who were involved in creating and selling bonds backed by mortgages to people with shaky credit. The bonds, whose real level of risk may not have been apparent to many investors, went sour, spreading losses throughout the financial system and helping to spark the global financial crisis in 2007-08. Among the biggest settlements: JPMorgan Chase agreed to pay $13 billion, Citigroup $7 billion and Goldman Sachs $5.1 billion.

Transatlantic crackdowns on big business didn’t start with Apple and Deutsche Bank. The EU competition regulators have taken on many — often U.S. — multinationals. Microsoft has struggled for years to address EU concerns that it was tying its own browser to its dominant Windows operating system and was fined 561 million euros in 2013. The European Commission has also gone after Google for allegedly abusing its dominant position in web searches and is investigating whether Amazon is rigging the market for e-book sales. The U.S. has already fined other big European banks, including HSBC for $1.9 billion in 2012 for allegedly helping launder money, including that of drug lords.

But the size of the most recent fines and penalties seems to have grown. To the point that Deutsche Bank’s finances were put in question when the U.S. settlement request was disclosed.

Peter V. Kunz, dean of the law faculty at the Institute for Business Law in Bern, Switzerland, is among those who think the Deutsche Bank case represents a tit-for-tat action: “The Obama administration is aware that in Europe, this issue with Apple is not something that will be decided in a short period of time.”

He said that the U.S. is looking to put pressure on the Europeans “by means of a legal attack. It’s clouded in a legal issue.”