Украинско-английский словарь - стежити

to watch, to have (to keep) one's eyes (up)on;to spy (up)on, to shadow (таємно в метою викриття);

стежити очима — to follow with one's eyes;стежити уважно — to watch closely (narrowly); to heed;за тобою стежать — they are on your trail; you are shadowed.