David Bermingham (C) and Giles Darby (R) paid US$100,000 bail

The men were released until next Friday but on the condition that they are tagged and remain in Houston. They all pleaded not guilty to the charges.

David Bermingham, Giles Darby and Gary Mulgrew will hear the full conditions of bail on 21 July. Their lawyers have argued they should return to the UK.

Their extradition has sparked a row in the UK over US powers to extradite.

Legal costs

As well as being electronically tagged and having their passports taken away, the three men - dubbed the NatWest Three - had to pay sums of cash to secure their freedom.

How US bail works

While Mr Bermingham and Mr Darby each posted bail of US$100,000 (�54,400), Mr Mulgrew put up US$20,000 plus shares in Glasgow Celtic football club.

Each man's lawyer made the case at Friday's hearing that they must be allowed to return to England to work in order to support their families and pay for legal costs.

Their defence case could take as long as two years to prepare.

But the prosecutor opposed their return to England, saying it could mean further extradition proceedings.

'Probable cause'

Prosecutors say that in 2000, the three men advised their former employer NatWest to sell part of a company owned by collapsed US energy giant Enron for less than it was worth.

They then left the bank and bought a stake in the company before selling it on at a significantly higher price, and making a huge profit, it is claimed.

They have been fighting extradition since they were arrested in 2004.

They say that extradition laws are unfair because the Americans have yet to ratify a treaty between the two countries.

The US only needs to outline an alleged offence and provide "evidence or information that would justify the issue of a warrant for arrest in the UK".

But British police must provide American courts with evidence of "probable cause" if they wish to extradite someone.

Mr Darby, from Lower South Wraxall in Wiltshire, Mr Bermingham, from Goring in Oxfordshire, and Mr Mulgrew, from Brighton in East Sussex, are accused of defrauding NatWest of over �1m each.