Those were the two droogies that Alax had attacked in the beginning of the movie to ensure that he remained the leader. Their names were Pete and Dim and they were seeking revenge on Alex now that they were police.
The short answer is that Alex was a tyrannical leader of his Drooges. He would often hit Dim and he found Billy to be repulsive.
Upset and downcast, Alex leaves without having a clear idea about his destination. On his way through the city he meets an old man who he and his gang had beaten up at the beginning of the first part and was given back what he deserved. Later, he encounters his former friend Dim with Billy-boy, another gang leader - both in the Police uniform. They take their revenge, too - Alex realizes he's quite defenceless against violence because it's better for him to suffer the punches than feel the terrific sickness that creeps over him any time he only imagines being violent himself.
Revenge is the key word here. In the dystopian world that Alex exits into after his "treatment", cops - even former mates - symbolize Burgess' vision of the world.
Return to FunTrivia
"Ask FunTrivia" strives to offer the best answers possible to trivia questions. We ask our submitters to thoroughly research questions and provide sources where possible. Feel free to post corrections or additions. This is server B184.