1. The surrounding of a stronghold with armed forces in order to bring about its capture or surrender: So many places are under besiegements by terrorist groups or those who are struggling to overcome such groups.
2. A crowd that is harassing somebody or an organization in an oppressive way with insistent demands or complaints: The office of the theater was finding it very difficult to provide enough tickets for all of the fans during their besiegements because there were too many who were striving to get tickets to see the popular movie star who was making a personal appearance when the film was over.