A search by U.S. authorities for Chinese researchers with ties to China’s military is leading to intensifying cat-and-mouse tactics involving what prosecutors say are foiled escapes, evidence tossed into a dumpster and a chase through an airport.

FBI agents have questioned dozens of researchers this summer about their work and military affiliations. In recent weeks, the widening operation has triggered efforts by some suspects to evade authorities and led to the arrest of at least two researchers whose work is allegedly tied to China’s military development, according to court filings by prosecutors.

In one case, a researcher at the University of California, Los Angeles studying artificial intelligence is accused by federal prosecutors of destroying evidence sought by the FBI in an investigation into potential technology theft. The researcher, Guan Lei, threw a damaged computer hard drive in a dumpster days after he was stopped from leaving the U.S. at Los Angeles International Airport, prosecutors allege.

In another, a scientist researching fluid dynamics at the University of Virginia is charged with stealing proprietary software code under development for two decades by his adviser, who received U.S. Navy funding. The adviser told investigators that Hu Haizhou, whom U.S. authorities prevented from boarding a flight in Chicago last month, hadn’t informed him he planned to return to China, prosecutors allege in filings in his case.

Messrs. Guan and Hu, arrested separately in late August, are in custody and have yet to enter pleas. A lawyer for Mr. Hu said that in his experience trade secrets charges are “typically overstated.” Mr. Guan’s lawyer didn’t respond to a request for comment. In an affidavit Mr. Guan filed in a related proceeding, he said he spoke with the FBI because he “had nothing to hide” and he believes he was targeted because of the “political climate between China and the U.S.”