UK Immigration Law
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They will be able to apply for a family permit in order to travel here with the EEA citizen and work. Once they are here they can stay apply for a registration certificate confirming their right to remain here for 5 years.
At the end of this time they can apply for permanent residence, which means they can they stay indefinitely. After obtaining PR they can apply for naturalisation provided they meet the eligiblity criteria
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EDIT. The EEA national must also come to the UK to exercise treaty rights (ie. work) in order for the non-eea national to travel here as above explained.