Lara Marlowe reports from Baquba, in eastern Iraq, where Badr Brigades and the People's Mujahedin occupy areas that US troops have not yet ventured into.
If US forces ever reach this city near the Iranian border, they'll have to arbitrate what must be the most absurd conflict engendered by the US-British invasion.
In Baquba, Iranian-backed Iraqis are fighting Iranians who were until this month backed by Iraq. The Iraqis are hiding from the Americans; the Iranians hope the US will support them. I trust I make myself obscure?
The Iranian-backed Iraqis are returning members of the Badr Brigades, a small army raised more than 20 years ago by the Iraqi Shia Ayatollah Mohamed Bakr al-Hakim, who lives in Tehran.
They fought against Iraq during the 1980-1988 war, then staged intermittent raids across the border. A week after Saddam Hussein's regime fell, several hundred straggled back into Baquba.
"The Badr Brigades came in pick-ups and land cruisers and mini-buses stolen from the government," said a school teacher.
"They took the weapons left by Iraqi forces. For a week, there was a lot of shooting between them and local people, until we realised they wouldn't hurt us; most of them were originally from here.
"Now they're holed up in three or four buildings. They are afraid of something - we don't know what - and they're getting ready for a fight. Maybe they're going to fight the munafiqin." Munafiqin means "hypocrites" in Farsi, and is the derogatory name used by Tehran for the People's Mujaheddin, a self-described "resistance group" who've been fighting what they call "the regime of the terrorist mullahs" for 22 years.
In 1987, Saddam Hussein gave them a piece of land the size of the Gaza Strip, 15 km north of Baquba. They named it Ashraf Camp, after a woman fighter killed by Revolutionary Guards in Tehran, and built a huge military base. Between April 10th and April 18th, the mujaheddin say 28 of their fighters were killed and more than 50 were wounded in clashes with the Badr Brigades.
Press reports estimate the Badr Brigades and the People's Mujaheddin have up to 10,000 fighters each, though I saw no evidence of such numbers. The mujaheddin claim returning Badr Brigades are an adjunct to 14,000 Iranian Revolutionary Guards dispatched across the border since Saddam Hussein fell.
US intelligence officials have evoked the far more modest figure of 12 Iranian agents in the south eastern city of Kut. In interviews yesterday in Baquba and Ashraf Camp, the mutual enemies agreed on two points: that the leader of the brigades, Ayatollah Hakim's brother, Abdelaziz, is in Iraq, and that Hakim's men are present in the cities of Kut, Amara, Nassiriya, Basra, Ramadi and Baghdad.
After a few gun battles, the residents of Baquba settled into fragile co-existence with the Badr Brigades and their political wing, the Supreme Council for Islamic Revolution in Iraq, which now rules the city of 200,000. The SCIRI claims to have established democratic local government, in consultation with 300 Arab tribal leaders. From Tehran, Ayatollah Hakim issued an appeal for unity between Shias and Sunnis.
In Baquba, Sayyid Ali Abdel Karim al-Madani, a Shia cleric, exercised swift Islamic justice this week, when two drunk men on a motorcycle shot dead four civilians. The criminals were turned over to the victims' families for execution.
A group gathered round me in the soukh to praise Sayyid Ali's decision, and the relative calm enforced by Ayatollah Hakim's men. But they spoke ill of the People's Mujaheddin ensconced in the military base north of their city.
"We don't like them, because Saddam allowed them to stay here," one said, to unanimous approval. "It's because of them that Iran used to bomb us." Local residents directed me to a building which they described as the headquarters of the Badr Brigades. Olive green military radios were stacked beside the door.
Gunmen were reluctant to let me enter, but a man with a hard, fox-like face who called himself Abu Hassan al-Timimi and said he was a member of the SCIRI eventually agreed to talk to me. A grenade launcher and boxes of hand grenades and ammunition sat on the floor. Mr al-Timimi said he had "no idea" where the Badr Brigades were. But he had an ultimatum for the People's Mujaheddin: "You are foreign, not Iraqi," he wanted to tell the Iranian rebels. "Either you go back to Iran, or you put your weapons down and surrender to the US coalition."
A few kilometres up the road, towards the Iranian border, I met two impeccably uniformed, infinitely polite People's Mujaheddin sentries. One of them gave The Irish Times instructions in Italian on how to reach an Iranian base inside Iraq. On the base, I was briefed by Ms Fatemeh Ramezani, of the "political department" of the People's Mujaheddin.
The group never received help from Saddam Hussein, she insisted. "We needed to be near Iran, to fight the regime of the terrorist mullahs.
"We were considered like an embassy, and we were completely independent." For more than two decades, the mujaheddin have pursued their lost cause with a passion bordering on fanaticism. They are an Islamic movement - women fighters wear headscarves and loose tunics over trousers - but say they want a secular, democratic Iran.
Seven mujaheddin were killed in the US bombardment of Iraq. At their hospital in Ashraf Camp, I saw three mujaheddin women who were seriously wounded when the US bombed one of their bases on April 8th; one had both legs amputated. But there are no hard feelings on the part of the mujaheddin, who dream the US will pick up where Saddam Hussein left off - supporting them in their fight.
US Brig Gen Vincent Brooks has acknowledged "negotiations undertaken by the Special Forces and coalition forces" with the Iranian rebels. They concluded a ceasefire, Gen Brooks announced. In the meantime, Tehran has threatened, if the US doesn't take care of the People's Mujaheddin, Iran will.
The US has warned Iran not to interfere in Iraqi politics. "Infiltration of agents to destabilize the Shia population would clearly fall into that category," a White House spokesman said.