Learn Hardcore German: Die Ärztin hat sofort helfen können, aber wir haben trotzdem warten müssen. - The female doctor was able to help immediately, but we still had to wait.

With a modal verb plus another verb, German uses the replacement infinitive (Ersatzinfinitiv) in the perfect: both the main verb and the modal appear as infinitives at the end, and you do not use the participle of the main verb. So the correct form is hat … helfen können, not hat … geholfen können. Without a modal, you would say Die Ärztin hat sofort geholfen.

Why are there two verbs at the end of each clause?

That’s the double‑infinitive cluster required by modal verbs in the perfect. The finite auxiliary (hat/haben) occupies the second position, and the two infinitives go to the clause‑final right bracket:

Die Ärztin hat sofort helfen können
wir haben trotzdem warten müssen

Why is there no zu before helfen or warten?

After modal verbs (können, müssen, dürfen, sollen, wollen, mögen), German uses the bare infinitive without zu. Hence helfen können and warten müssen, not zu helfen können or zu warten müssen.

Why do we use haben as the auxiliary and not sein?

With modal + infinitive, the auxiliary is always haben in the perfect, regardless of whether the main verb would normally take sein on its own. So you say er hat gehen müssen, not er ist gehen müssen.

Can I say this in the simple past instead?

Yes, and it’s very natural—especially for modal verbs:

Die Ärztin konnte sofort helfen, aber wir mussten trotzdem warten. In spoken German, the perfect is very common, but modals in the simple past are also widely used.

Is it okay to use both aber and trotzdem, or is that redundant?

It’s idiomatic and common. Aber coordinates the second main clause; trotzdem is a concessive adverb meaning in spite of that. You can also use just one:

With both: …, aber wir mussten trotzdem warten.
Just concessive adverb: …, trotzdem mussten wir warten. Some style guides suggest avoiding the combination as pleonastic, but everyday German uses it freely.

Could I use obwohl instead of aber … trotzdem?

Yes—switch to a subordinate clause:

Die Ärztin hat sofort helfen können, obwohl wir trotzdem warten mussten. (Typically you’d drop trotzdem here) More idiomatic without trotzdem:
Die Ärztin hat sofort helfen können, obwohl wir warten mussten.

Why is there a comma before aber?

Because it separates two independent main clauses. In German, a comma before aber is mandatory when it connects main clauses.

Why Ärztin and not Arzt?

Ärztin is the feminine form of Arzt (doctor). The suffix -in marks the female profession title; the plural is Ärztinnen. All nouns are capitalized in German, hence Ärztin with a capital A.

Where can sofort go in the sentence?

Common, natural placements include:

Die Ärztin konnte sofort helfen.
Die Ärztin hat sofort helfen können.
For emphasis: Sofort hat die Ärztin helfen können. Putting sofort after the verb cluster (… helfen können sofort) is unusual and sounds wrong in standard German.

Why is the order warten müssen (main verb before modal) and not müssen warten?

In the perfect with modal verbs, the standard order in the double‑infinitive cluster is main verb first, modal last: warten müssen, helfen können. Variants like haben müssen warten occur regionally, but the standard form is haben warten müssen.

Can I say hat gekonnt helfen or hat helfen gekonnt?

Standard German prefers the replacement‑infinitive form hat helfen können. Using the participle of the modal (gekonnt, gemusst) together with another infinitive is generally avoided in standard usage. The participle of a modal is used when the modal stands alone, e.g., Sie hat es gekonnt.

Why does müssen change from ü to u in the past (mussten) and können to konnte?

Modal verbs are irregular and undergo vowel changes in the simple past:

müssen → musste(n)
können → konnte(n) This is normal and needs to be memorized.

How would I add the person being helped? Does helfen take a direct object?

Helfen takes a dative object, not an accusative one. For example:

Die Ärztin hat der Patientin sofort helfen können. (helped the female patient)
Die Ärztin konnte dem Patienten sofort helfen. (helped the male patient)

Could I move trotzdem to the front of the second clause?

Yes, for emphasis or flow:

…, trotzdem haben wir warten müssen. With aber, both are possible:
…, aber trotzdem haben wir warten müssen.

Is there any difference in meaning between the perfect and simple past here?

Not really in content. It’s mainly stylistic and regional. The perfect (hat … helfen können / haben … warten müssen) is very common in speech; the simple past (konnte … / mussten …) is frequent with modals and in writing.