Simple infinitive: I/m happy to be here
Perfect infinitive: Ali seems to have been ill a lot
Continuous infinitive: The girl seemed to be waiting for someone
Perfect continuous infinitive: She seemed to have been waiting here for hours.
Passive infinitive: My computer is supposed to be repaired today.
Perfect passive infinitive: It was supposed to have been repaired last week.
1) We use the Perfect infinitive when we want to be clear that we are talking about an earlier time or a completed action.
2) We use the Perfect infinitive after would plus like, hate, love or prefer when we talk about earlier events.
a) I would like to have been here.
b) You would hate to have seen all the destruction.
3) We can use the Continuous infinitive for an action in progress
4) We can use the perfect Continuous infinitive for an action in progress at an earlies time.
5) We can use the Passive infinitive for present or future actions happening to the subject.
6) We can use the perfect Passive infinitive for earlier actions.
Simple gerund: I don’t mind waiting
Perfect gerund: She regretted having told us about the money.
Passive gerund: She wrote in her book about being punished as a child.
Perfect passive gerund: She still has nightmares from having been locked up in a small dark cupboard.
1) We can use the perfect gerund when we want to be clear that the action was in the past.
2) We can use the passive gerund for an action which happens to the subject.
3) We can use the perfect passive gerund to emphasize that the action happened in the past.