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Modal auxiliary verbs form their past participle using the same stem as for the simple past:
Unsere Kinder haben das nie gedurft. |
Our children were never permitted (to do) that. |
This form of the past participle appears only when the modal auxiliary is used alone, which is infrequent.
More often, the modal is used in conjunction with another verb, and the past participle becomes part of a double infinitive construction.
Unsere Kinder haben nie fernsehen dürfen. |
Our children were never permitted to watch television. |