Study materials
These sentences use the same pattern as must have done, but the chain is longer.
She must have been waiting for hours.
She has probably been waiting for hours.
The file might have been deleted by mistake.
Perhaps someone deleted the file by mistake.
We could have been killed!
We could have died!
The logic is the same as in the short forms: the modal, have and the third form. The third form is now been, followed by -ing or another third form. The article explains the continuous form after a modal verb for the present and the past, and the passive form.
Continuous and passive after a modal
A modal verb need not be followed by a simple action. Be with -ing shows a process, been with -ing a process in the past, and be or been with the past participle forms the passive, an action done to the subject.
She must be working late again.
They must have been arguing.
It looks as if they were arguing.
We should have been told earlier.
Passive.
He can't have been invited.
He could not possibly have been invited.
Been with -ing
When you guess about a process that went on rather than one event, have is followed by been and the -ing form.
They must have been arguing. Her eyes were red.
He can't have been sleeping. I heard music from his room.
You should have been resting, not working.
Compare. She must have worked hard says the work happened. She must have been working all night stresses how long it went on. State verbs like know, own or believe are not usually used with -ing, so must have known, not must have been knowing.
Been with the third form
If the subject does not do the action but receives it, the passive is needed. Have is followed by been and the third form.
The letter must have been sent last week.
This should have been checked before printing.
The window can't have been opened from outside.
A letter does not send itself, so must have been sent, not must have sent. The passive with should have is also popular because it does not name who is to blame. Should have can also express expectation here: The pizza should have been delivered by now, meaning by plan it was due.
Common mistakes
The first mistake is a missing been before -ing.
She must have waiting for hours. → She must have been waiting for hours.
Been stands between have and -ing.
The second mistake is an active form where the passive is needed.
The letter must have sent last week. → The letter must have been sent last week.
A letter does not send. It is sent.
The third mistake is -ing from a state verb.
He must have been knowing the answer. → He must have known the answer.
Know describes a state, so no been and -ing.
The first and second mistakes show right after have. If -ing follows, been must stand before it. If the subject does not do the action, have is also followed by been and then the third form. The third shows in the verb itself. Know, own or believe describe a state and are not usually used in the continuous.