European Central Bank officials are expected to cut interest rates this week for the first time in more than five years, drawing a line under the worst of the eurozone’s inflation crisis and easing the pressure on the region’s weak economy.

But as policymakers in the eurozone move ahead, they leave behind their counterparts at the U.S. Federal Reserve, who are grappling with a seemingly more persistent inflation problem and warning that it will take longer to cut rates there.

Lowering interest rates in Europe before the United States does would create a gap between the policies of two of the world’s largest and most influential central banks. A move by the E.C.B. to ease its policy could weaken the euro, while higher interest rates in the United States would continue to tighten financial conditions there and in other countries because of the global role of the dollar.

Some analysts have questioned how far the E.C.B. can split from the Federal Reserve, while others say a divergence is not unusual and reflects two different economic situations.

“We are coming from more than a yearlong stagnation” in Europe with signs that disinflation is on track, said Mariano Cena, an economist at Barclays. “This is a very low starting point for an economy.”

By contrast, the U.S. economy has been booming over the past few quarters.

“There has already been divergence in the economies,” he said. “So if there is divergence in policy, it’s because it follows the different trajectories of the economies.”