Tayside Police refuses to reveal the identities and locations of the offenders, but said the information is known to the relevant bodies.

This latest revelation follows the high-profile case of Thomas Shannon, who in August escaped from a Lochee flat in which he was subject to round-the-clock super-vision, following his release from Polmont Young Offenders Institution.

Seventeen-year-old Shannon had been jailed in 2006 after being convicted of assault with intent to rape.

Local people and councillors reacted with fury amid claims they had been kept in the dark about Shannon’s presence in the community.

Subsequently three Lochee councillors, including Lord Provost John Letford, were told they had no right to be briefed when sex offenders were placed within their ward — regardless of any risk posed.

Councillor Letford said the latest development posed serious questions about the supervision system.

“It’s a huge concern to learn that not only are there other dangerous sex offenders living in Dundee, but they have managed to escape supervision.

“The recent meeting between councillors and the Multi-Agency Public Protection Arrangement saw the system being vigorously defended by those in charge of its policing, but this surely must now pose serious questions about just how effective it is.

“It was made plain that under no circumstances would councillors be informed when sex offenders are moved into the community, and the fact they’re apparently not being effectively managed will be very worrying for the public.”

These offenders are managed in the community by MAPPA, which is used to support supervision of the “most serious” sexual and violent offenders. Members include police and social workers.

Detective Super-intendent Roddy Ross, MAPPA’s Tayside Police representative, suggested the fact supervision orders were breached was not surprising.

“Sexual Offences Prevention Orders are not handed down lightly by the courts,” he explained.

“By their very nature, they’re given to offenders considered to be at a very high risk of re-offending.

“The purpose is to give these offenders a chance to comply with the court and be tested within the community.”

Asked whether community supervision arrangements were up to scratch, given the 100% breach rate, Mr Ross said the offenders weren’t watched 24 hours a day.

“We have to remember they’re not in prison. Other authorities have decided they should be at liberty.

“All these orders allow us to do is restrict their liberty while they’re readjusting to life among other members of society.

“The management of these offenders is tricky, and we can’t always be 100% confident we’ve got it right, but Sexual Offences Prevention Orders ensure any problems are dealt with quickly.”