Foreign fighters in Ukraine, many in motley groups, face perils if captured.

Over the last few weeks, a number of the thousands of foreign volunteers who flocked to join the fight against Russia have gone missing or have been captured.

Last week, two Britons and a Moroccan who were taken prisoner while fighting for the Ukrainian armed forces were sentenced to death in Russian-occupied eastern Ukraine, after being accused of terrorism.

This week, two Americans fighting with a group of foreign soldiers went missing in action near Kharkiv, Ukraine’s second-largest city, which is about 25 miles from the Russian border. Their families fear they have been captured, having disappeared after the platoon came under fire.

The missing and captured fighters have focused attention on the thousands of largely unregulated volunteers in Ukraine, only some of whom have been accepted into the Ukrainian Army’s International Legion.

The platoon that the missing Americans belonged to was one of dozens of loosely organized volunteer outfits that have absorbed foreign veterans, including many Americans. The volunteers have proved to be both valuable assets and at times an unruly problem for Ukraine, and present a potentially difficult challenge for their home governments if they are caught or captured.

On Friday, President Biden said that he had been briefed on the two Americans reported to be missing in Ukraine, and that the administration does not know of their current location.

“I want to reiterate: Americans should not be going to Ukraine now,” he said.

The International Legion, formed after President Volodymyr Zelensky of Ukraine issued a call in late February for foreigners to help fight, is considered the most selective of the foreign groups.

Damien Magrou, a French-Norwegian lawyer who is the spokesman for the Ukrainian military’s International Legion, said in an interview in April that he felt the war had “struck a chord” among many American veterans.

“There are also a lot of American vets who feel they can make a difference because the U.S. has been involved in a lot more conflicts in the last 20 years than European countries,” he said.

Mr. Magrou, a corporal in the legion’s structure, said accepted volunteers are now required to have combat experience, no records of dishonorable behavior, and no membership in extremist groups. Other groups are not as selective, he said.

Mr. Magrou said he encourages volunteers rejected by the legion to take a shuttle bus provided by the military back to the Polish border. But, he added, “they are legally in the country and we can’t force them to do anything.”

Russia maintains that some of foreign fighters it has captured are mercenaries and not entitled to protection as prisoners of war under international law. A local court in the Russian-occupied Donetsk region found that the two British and one Moroccan fighters, who had immigrated to Ukraine, were guilty of “training for the purpose of carrying out terrorist activities” and that they undertook their activities “for a fee.”

It remains unclear what missions were carried out by the group whose American members went missing, or who in the Ukrainian armed forces or the government oversaw them and gave them orders.

The American veterans who are missing are Alex Drueke, 39, a former U.S. Army staff sergeant who served in Iraq, and Andy Tai Ngoc Huynh, 27, a former Marine, family members said. They disappeared when their platoon came under “heavy fire” in a village on June 9, leading all its members to fall back except for the two of them, according to a statement sent by Mr. Drueke’s family. Reconnaissance by foot and drone did not turn up any sign of the two soldiers, the statement said.

The Geneva Conventions, which govern the law of war and which Russia has signed, specify that captured volunteer fighters can also be considered prisoners of war. The primary definition of a mercenary under international law is someone fighting primarily for financial gain who is paid substantially more than local armed forces.

Those who join the International Legion are paid the same amount as their Ukrainian military counterparts. They receive a basic salary, equaling about $630 a month, with bonuses that can reach several thousand dollars a month.

Some fighting with other groups are given one-time payments to defray their expenses, while others are unpaid.

Lawrence Hill-Cawthorne, an associate professor of law at the University of Bristol, said that even volunteer fighters not embedded in the Ukrainian military would be entitled to P.O.W. protection if they are openly carrying arms while fighting.