They both took responsibility for the attacks on the websites of UK's Serious Organised Crime Agency and the National Health Service, as well as those belonging to News International, Nintendo, Sony, the CIA, the US Air Force, and many others.
Cleary also admitted to having hacked into US Air Force Agency computers.
Still, both of them adamantly denied stealing confidential data and posting it online on Pirate Bay, Pastebin or on the group's own website.
Two other individuals - 25-year-old Ryan Ackroyd (aka "Kayla") and a 17-year-old boy - have also been charged during the same proceedings at Southwark Crown Court on Monday, but have denied taking part in the attacks against those websites.
All four are scheduled to go on trial in April 2013. In the meantime, all except Cleary were released on bail.
According to Cleary's lawyer, it seems that US prosecutors will not be asking for him to be extradited to the US if he faced charges in the UK.
Reading our newsletter every Monday will keep you up-to-date with security news.
Receive a daily digest of the latest security news.