To conjugate modal verbs in the Perfekt, we still need the auxiliary “haben” (conjugated with the subject). The difference here is made by the two infinitives at the end of the sentence. That is why we call this “double infinitive”.
1. Modal Verbs in the Present tense.
When using modal verbs in the present tense in German, we must remember that their conjugation pattern is irregular, and that they are typically used with another verb in the infinitive, which moves to the end of the sentence or clause.
Examples:
Ich muss ihn heute anrufen. I must call him today.
Wir können morgen losfahren. We can depart tomorrow.
2. Modal Verbs in the simple past (Präteritum)
When forming sentences in the simple past (Präteritum), we need to use the simple past conjugation of the modal verb, but the second verb will stay in the infinitive and remains at the end of the sentence.
Examples:
Ich musste ihn heute anrufen. I had to call him today.
Wir konnten gestern losfahren. We were able to depart yesterday.
3. Modal verbs in the present perfect (das Perfekt)
All modal verbs use “haben” to form the present perfect. They each have a participle, as they can be used without an accompanying infinitive, in which case they act like irregular strong verbs.
Examples:
Ich habe das gedurft. I was allowed (to do) that.
Sie hat es gemusst. She had to (do it).
When the modal verb is associated with another verb in the sentence, we need to form a double infinitive, with the modal verb in the infinitive at the very end, preceded by the other verb in the infinitive.
Examples:
Ich habe ihn gestern anrufen müssen. I had to call him yesterday.
Wir haben es nicht wissen können. We could not have known that.
In subordinate clauses, the conjugated form of “haben” does not go to the very end; it stands directly in front of the double infinitive: Ich weiß, dass sie ihre Eltern hat besuchen wollen. I know that she wanted to visit her parents.