1) Exercising surveillance 
• (a.) Overseeing; watchful. • (n.) One who watches over another; an overseer; a spy; a supervisor.
Sur·veil'lant noun ; plural Surveillants . [ French, from surveiller to watch over. See Surveillance .] One who watches over another; an overseer; a spy; a supervisor. 
surveillant 1. Overseeing; watchful. 2. Someone who watches over another; an overseer; a spy; a supervisor. 3. A person who exercises surveillance.
exercising surveillance.