In a famous Midrash in Shab. 87a-b, the angels object to the Torah being given to humans, until Moshe proves that it is only relevant to humans because of their nature. In one example, he asks rhetorically, "Do you (angels) have jealousy (that might lead you to kill or covet)?"
Well, to be honest, they were acting rather jealous. So, do angels have jealousy?