The designation given to agents who turn against their original controllers and witch their allegiance to their supposed target. Some agents may arrange for their recruitment by their intended, ultimate target, and whatever their motivation the description remains valid. The fact that a spy happens also to be an intelligence officer does not make him (or her) a double agent, so it is erroneous to apply this term to Kim Philby, George Blake, Geoffrey Prime, Oleg Penkovsky, Aldrich Ames, or Robert Hanssen. In all those cases, the spies were run as agents by a hostile intelligence agency.
Triple agents are usually double agents who are deployed againstan adversary for the precise purpose of having them ostensibly recruited as double agents.