The continuous infinitive is used to express a continuing action after a verb or auxiliary which must be followed by the infinitive. The continuous infinitive is formed:
to be + present participle
As with the present infinitive, there are situations where the zero form of the continuous infinitive is required, so the word to is omitted. This happens after most modal auxiliaries, and in other places where zero infinitives are used.
- I'd really like to be swimming in a nice cool pool right now.
- I happened to be waiting for the bus when the accident happened.
- It must be nice to be going to a wedding overseas.
- You must be joking!
- We should be hurrying. We're late!
- You'd better be working on your report when I get there.