A 15-year-old boy has also been charged with attempted criminal damage and riotous behaviour.
Both teenagers are due to appear at Derry Youth Court later today.
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Elsewhere, police in Belfast have arrested a man on suspicion of possessing and making explosives.
The 54-year-old was detained following the search of a residential property in the Braniel area of the city on Thursday night.
It follows a number of security alerts in Belfast in recent days which have been linked to the new East Belfast GAA club.
The PSNI are treating the incidents as a "sectarian hate crime" and are urging members to check their cars and report anything suspicious to them.
