The Perfect Infinitive Continuous

Using the perfect infinitive continuous is a good way to make your spoken or written English more interesting and pleasant to the listener/reader. Let's first have a look at how to form it:

Form

to have been + present participle

Example: He seems to have been cheating both of us.

Use

It is generally used  after auxiliary verbs and after appear and seem, but it can also be used after happen, pretend and the passive of believe, know, report, say, understand:

1.
He says he was dacing with Jane.  He couldn't have been dancing with her. Jane wasn't at the party.

2.
a) I was following Mike closely.

b) You shouldn 't have been following
him closely; you should have left a good space between the two cars.

3.
He appears to have been sitting there a long time  =
It appears that he has been sitting there a long time.

4.
He pretended to have been studying  =
He pretended that he had been studying.