A third soldier had already pleaded guilty to one charge of assault after he was pictured standing on a detained Iraqi looter.
The abuse by the soldiers from the Royal Regiment of Fusiliers was captured in a series of photographs that were published around the world after they were released as evidence in the case.
Shortly after the five-week trial began at a British barracks in Germany last month, British Prime Minister Tony Blair described the photographs as "shocking and appalling".
Images showing an Iraqi suspended from a forklift truck and others of two men forced to simulate sex acts were reminiscent of pictures depicting the abuse of Iraqi prisoners by American guards at Abu Ghraib, the notorious prison near Baghdad.
The mistreatment in this case took place after British troops rounded up looters who were stealing powdered milk from a humanitarian aid depot known as Camp Bread Basket, near the southern Iraqi city of Basra, in May 2003.
The most senior of the three accused, Corporal Daniel Kenyon, 33, was found guilty on Wednesday on two charges of failing to report that soldiers under his command had abused Iraqis, including the incident in which two naked men were forced to simulate sex.
He was also found guilty of aiding and abetting another of the accused in beating a detainee.
Corporal Daniel Kenyon (R) now
faces a prison sentence
Judge Advocate Michael Hunter postponed sentencing until Friday but said Kenyon would face a jail sentence of up to two years.
The seven British officers acting as a jury also found Lance Corporal Mark Cooley, 25, guilty of suspending a bound Iraqi from the forklift truck and of simulating a punch on an Iraqi for a photograph. The judge said he faces up to two years in prison.
Lance Corporal Darren Larkin, 30, had pleaded guilty to assault after he was pictured standing on an Iraqi and faces a possible six-month prison sentence.
An additional charge against Cooley of simulating a kick for a photograph was dropped during the court martial.
Geneva Conventions breach
A charge against Larkin of forcing the detainees to undress was also dropped.
The trial heard that the soldiers' commanding officer, Major Dan Taylor, had ordered his men to detain looters and "work them hard" after the camp was plagued by repeated intrusions in the chaotic weeks after the fall of Iraqi leader Saddam Hussein.
Prosecutors said this order was in breach of Geneva Conventions.
There was outrage in Iraq after
the photos were published
The photographs of the abuse came to light when Gary Bartlam, a soldier not accused in this case, left them for processing at a shop in England. A shop worker called the police after seeing the images.
Bartlam had been due to stand trial alongside the three soldiers but his lawyers negotiated a plea bargain which saw some of the charges against him dropped in return for him giving evidence in this trial.
In a separate court martial this year, Bartlam admitted taking photographs of the Iraqis simulating sex and was sentenced to 18 months in a youth detention centre and disgracefully discharged from the British Army.
The British Ministry of Defence said it would not comment on Wednesday's verdict until sentences had been handed down.