Six British cavers held by Mexican authorities after being trapped in a flooded cavern are hoping to fly back to the UK on Monday.
The cavers have denied doing anything wrong
The men were detained over possible visa irregularities and immigration officials have until 0700 local time (1400 BST) to question them.
A separate probe into claims the cavers were looking for uranium was dropped by prosecutors in the country on Sunday.
One of the group, Jonathan Sims, 41, said the men had done nothing wrong.
He said they had been detained because of "bureaucratic incompetence and inefficiency".
The cavers could be deported, barred from returning for several years, face fines of up to 3,000 pesos (£180) or jailed for 18 months if found to have broken immigration rules.
The six potholers are being held in an immigration detention centre along with seven more team members who had stayed above ground at the cave site.
Mr Sims, now a businessman based in Shanghai, whose parents live in West Sussex, said: "We have been through all this investigation with the justice department and the immigration department and all the indications are that we have done absolutely nothing wrong at all.
"Seven am tomorrow morning is a fairly important deadline for the Mexican authorities and if they do not come up with something then, it's just going to cause even more embarrassment for them.
"We are hoping that we might have eight or 10 hours of British Airways hospitality tomorrow afternoon.
"That's what we are hoping for and that's what we are looking forward to," he told ITV News on Sunday night.
The cavers were not thought to have been in danger
The men were arrested on suspicion of entering Mexico illegally after their rescue from the flooded cavern near Cuetzalan.
Mexico's President Vicente Fox intervened in the affair, saying he was unhappy with explanations for their activity in the caves, where they became trapped by floods.
But Mr Sims' father Alan, who was hoping his son would be back home on Monday morning, said the group were merely on "a fun holiday".
He added: "The Mexican government actually write down what the requirements are for tourism visas and unless it is a historical site or if they want to take samples out of the cave when they need a different kind of visa, a tourist visa is what they all have.
"There about 50,000 cavers a year going to those caves.
Jonathan has been going to those caves for 14 years."
The men were members of a 13-strong team from the Combined Services Caving Association (CSCA), and four are serving in the British military.
They are Sgt John Roe of the RAF, Navy
Warrant Officer Charles Milton and Sgt Chris Mitchell and Capt Toby Hamnett from the Army.
The other two were retired Mr Sims and civilian caver Simon Cornhill.
The cave exploration, which began last Monday, was due to last 36 hours but the group got stuck after heavy rain raised the water level in the cave.
They declined local offers of rescue, instead preferring to wait for two specialist British divers who flew to Mexico to escort them out.