1. Is 'had to' the past of 'must'? Yes. 'Must' itself has NO past tense form. It only exists in the present simple. For all tenses and aspects other than present simple, we use 'have to'. For example: Present simple: I must work = I have to work Present continuous: I'm having to work Past simple: I had to work Present perfect: I've had to work Future: I'll have to work or I'm going to have to work 2. Is 'must have' + pp' the past of 'must'? No. "He must have gone" is NOT the past of "He must go". The past of "He must go" is "He had to go". When we say "He must have gone", we are using the modal verb 'must' to make assumption about something which we believe to have happened in the past. The words 'have gone' are a perfect infinitive. 'Gone' refers to a possible past event, while the modal verb 'must' is in the present tense: it can only ever be in the present, because it has no other form.

If you wanted to say something like; “I must eat” in the past you could say “I had to eat”. On the other hand if you say “I must have eaten” it means you strongly believe that you ate not that you had a need to eat.