May and let

think that we will all be driving hovercars by the year 2000, whereas at a later date it might be reported that In 1960, people thought we would all be driving hovercars by the year 2000.

This "future-in-the-past" usage of would can also occur in independent sentences: I moved to Green Gables in 1930; I would live there for the next ten years.

In many cases, in order to give modals past reference, they are used together with a "perfect infinitive", namely the auxiliary have and a past participle, as in I should have asked her; You may have seen me. Sometimes these expressions are limited in meaning; for example, must have can only refer to certainty, whereas past obligation is expressed by an alternative phrase such as had to (see Replacements for defective forms below