My daughter is a German (EU) citizen: will her new SA husband be allowed to live in The Netherlands with her?
Yes. He can move there under EU free movement (here, "EU country" generally includes non-EU members of the Schengen area):
If you are a worker
If you are working in another EU country, as an employee, self-employed or on a posting, your non-EU spouse, dependent children and grandchildren can stay there with you without having to meet any other conditions.
If you are a pensioner
If you are a pensioner living in another EU country, your non-EU spouse, children and grandchildren can stay there with you if you have for yourself and your whole family:
- sufficient income to live without needing income support
- comprehensive health insurance in that country
If you are a student
If you are a student living in another EU country, your spouse, dependent children and grandchildren can stay there with you if you:
- are enrolled in an approved educational establishment
- have sufficient income to support your whole family without needing income support
- have comprehensive health insurance for your whole family in that country
Your non-EU spouse, children and grandchildren must apply for a residence document with the authorities in the host country (often the town hall or local police station) within 3 months of arriving.
Find out how to get a residence card for your non-EU family members.
During their stay in your new country, your non-EU spouse, children and grandchildren should be treated as nationals, notably regarding access to employment, pay and benefits facilitating access to work and enrolment in schools.
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As noted in a comment, this applies in general to non-EU family members of EU citizens when moving to an EU country other than the country of citizenship. It also applies when moving to the EU country of citizenship from another EU country.