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Past modals come in two forms. The first type is the easiest and usually requires only a simple word change:

Past Modals

Past modals come in two forms. The first type is the easiest and usually requires only a simple word change:

I can drive.	(present ability)
I could drive when I was 16.	(past ability)
I have to go to California.	(present obligation)
I had to go to California.	(past obligation)
Lenny will pay tomorrow.	(future intention)
Lenny said he would pay tomorrow.	(future reported from the past)

Past modals with "have"

Some past modals can be formed by using have + the past participle of the main verb immediately after the modal. (should have, could have, would have, etc.)

However, since modals express possibility, intention, obligation, etc., they do not always indicate a definite tense. Therefore, when using past modals with have, special meanings need to be considered.

I should go to the funeral.	(I feel an obligation to go later.)
I should have gone to the funeral.	(I didn't go. Now I regret it.)
Lex might take Karen to the airport.	(It's a future possibility.)
Lex might have taken Karen to the airport.	(He may be on his way there now.)
Lex could have taken Karen to the airport.	(Most likely he didn't.)
Lex would have taken Karen to the airport.	(He didn't. He had an excuse.)
Otis didn't come to work yesterday.	(past fact)
He had to take care of his children.	(past obligation)
His children must have been sick.	(conjecture about the past)