Portuguese police are questioning 11 people as part of the investigation into the disappearance of Madeleine McCann in 2007.
They are being observed by Met Police detectives who arrived in Faro earlier.
Among the witnesses due to be questioned over the next three days is British ex-pat Robert Murat.
Mr Murat, who is not a suspect, was first questioned when three-year-old Madeleine went missing from the Algarve resort of Praia da Luz seven years ago.
He was cleared of any wrongdoing and won substantial damages from British newspapers over how he was portrayed at the time.
Along with Mr Murat and his wife, police are expected to question two other British people and seven Portuguese citizens.
Last month, Mr Murat told the BBC: "My conscience is clear and I have no problem speaking to the police again."
The BBC has learnt that of 10 people of interest that British police have requested be interviewed by Portuguese police in Faro, three are being questioned on Tuesday, four on Wednesday - including Mr Murat - and three on Thursday.
The 11th person is a woman who is currently in the UK and will be questioned there at a later date.
Some of the interviewees are former employees of the Ocean Club where the McCanns were staying when Madeleine went missing, BBC correspondent Christian Fraser said.
He added that police would be looking for "inconsistencies" with any answers witnesses gave seven years ago.
Thursday 3 May 2007: Timeline
- 20:30 Kate and Gerry McCann leave their apartment to have dinner at a Tapas bar
- 21:05 Gerry McCann checks on Madeleine and her siblings
- 22:00 A man is seen carrying a child wearing pyjamas heading towards the ocean
- 22:00 Kate McCann raises the alarm that Madeleine has gone missing
In Portuguese law, if officers suspect an individual's involvement in a crime but are not in a position to arrest or charge, they are given "arguido" status - giving them the right not to answer questions and to legal representation.
Police from the UK have supplied more than 250 questions for Portuguese police to ask the 11 witnesses.
At the scene
By Duncan Crawford, BBC News
A huddle of camera crews and photographers surrounded Det Ch Insp Redwood as he walked up the narrow cobbled street outside the police station in Faro.
He was repeatedly asked questions but didn't make any statement about the case.
After years of rumours and suspicion, some residents in Praia da Luz, the resort where Madeleine went missing, feel the focus on the case has gone on for too long.
A few "Stop" road signs in the area now have graffiti that reads: "Stop McCann Circus".
Earlier this year detectives from London flew to the Algarve to assist with searching scrubland near the resort where Madeleine disappeared. They did not uncover any evidence.
The Met's Operation Grange was set up in 2011 after Prime Minister David Cameron asked the force to "bring their expertise" to the inquiry following a request from Kate and Gerry McCann.
Former detective Mark Williams-Thomas said Portuguese police would now be "tracing, interviewing and eliminating" witnesses and suspects.
"What the British police are doing is going through all the documentation they've had from the Portuguese, as well as what they've collected themselves," he told BBC News.
"But of course this is problematic because it's not a British inquiry and there is real sensitivity. It's almost like treading on egg-shells because... another force is coming in and saying 'we don't think you did the inquiry very well, we think we can do it better'."
He said the British police involvement had now cost £8m and ideally a permanent team of officers would work hand in hand with their Portuguese counterparts.
"The sad reality is that until we know what's happened and either an offender has been caught or Madeleine has been found, we aren't any further forward," he added.