Portuguese police have given two press conferences

In particular, British commentators have criticised their refusal to give out more information about any possible suspects.

The police say they are operating within the constraints of Portuguese law and cite differences in the Portuguese system compared to the British for the complaints.

BBC News looks at those differences.

What is the UK protocol when a child goes missing?

Police universally agree that the first few hours are crucial in the hunt for a missing child and, by and large, British police give out as much information quickly as they can to help find them.

In March last year, every British force signed up to the Child Rescue Alert (CRA) scheme.

This is a system to publicise suspected abductions of under-18s where there is a fear they could be at imminent risk of serious harm or death.

It gives urgent messages to television and radio stations, usually with descriptions, last known whereabouts and information on any suspects.

CRA is based on a US scheme called Amber Alert - after nine-year-old Amber Hagerman, who was abducted, raped and murdered in Texas in 1996.

It issues missing alerts via traditional media as well as by e-mail, text message and on road traffic information signs.

The Association of Chief Police Officers (ACPO) advises forces to treat every missing person case as a major crime investigation.

Its guidance reads: "It is always easier to rein back from the early stages of a major inquiry than it is to recover missed opportunities resulting from miscalculating in the early stages.

"In cases where the circumstances are suspicious or are unexplained, use the maxim: If in doubt, think murder."

Why don't Portuguese police release more information to the media and the public?

All criminal cases in Portugal - and elsewhere in much of Europe - are governed by the law of judicial secrecy.

This means that once a criminal investigation is under way, police cannot reveal anything about that investigation, including any details about potential suspects.

Any leaks could jeopardise a trial.

The BBC's Alison Roberts, in the Algarve, explains that normally this secrecy is not an issue because the Portuguese media are used to it and know not to bother asking questions.

Local people have joined police in searching for Madeleine

Problems can arise though, she says, as with information about Madeleine's clothing, when there is confusion about whether something is already in the public domain.

And if a detail has come from a different source - such as the family involved - can police then discuss it openly even if it falls under the secrecy law?

This grey area, our correspondent says, could help explain the second press conference held by police on Monday.

At the first media briefing on Saturday, the police may have felt they started to go down a road they shouldn't have - towards saying too much - Ms Roberts said.

Then in the second conference they tried to rein the situation back in, she added.

There has been surprise in some Portuguese quarters that police have even said as much as they have and there can be serious repercussions for breaking the secrecy law.

In a recent case of political corruption, police raided a newspaper and seized computers after reporters gained information about an ongoing investigation.

How is the police system structured in Portugal?

Like much of Europe, there are tiers of police in Portugal.

Firstly, there are two local branches run by the Interior Ministry. The PSP operate in urban areas like Lisbon and Faro, and the GNR cover more rural places like the Algarve.

Madeleine's mother Kate McCann appealed directly to her captor

The BBC's Alison Roberts says the GNR are the national guard and the equivalent of the French gendarmes.

They would have been the first port of call for Madeleine McCann's parents when they found her missing.

However the GNR do not get involved in criminal investigations - currently their role is to co-ordinate searches, man cordons, etc.

Once it is apparent that a case is criminal, the detective force, or policia judiciara, must be called in.

This force operates under a completely different government department, the Ministry of Justice.

Portugal also operates a system of investigating magistrates who carry out the later stages of a criminal investigation.

They interview suspects and witnesses, but only once police have gone through a formal process of naming someone as a suspect, then naming him as the accused, and so on.

The Portuguese police say they are working closely with Europol. What is the role of Europol?

The agency's role is to link up different countries to assist criminal investigations.

It only acts on request and can only become active when two or more member countries are involved - in this case Britain and Portugal.

But the Europol website states "there must be factual indications that an organised criminal network is involved".

One Portuguese newspaper, Publico, claims police suspect Madeleine's disappearance could be linked to a group selling children for international adoption.

Another paper, Correio da Manha, said an international paedophile ring, probably based in Britain, could be responsible.