In court on Tuesday, Barry Reid, 40, described as a prisoner at Barlinnie, admitted that while one youngster under 13 was sleeping in December 2012 he handled her clothing and attempted to pull down her trousers.
And he admitted the assault on the second, also aged under 13, in April last year by entering her bedroom and handling her underwear.
In addition, Reid pleaded guilty to breaching in 2012 a sexual offences prevention order prohibiting him from entering any residential address where any child or young person under the age of 18 is known by him to reside.
The case was this week continued to April 19 for background repots.