Les Algériens, les Saoudiens. I'm not very sure about the last one, it is correct but there are perhaps other way to denominate them.
I'm more sure about saoudien as an adjective: personnes de nationalité saoudienne
I don't think there is another way Valerie. Les saoudiens is the correct word I think. I have a friends who lived in Saudi Arabia, the words Saoudi ou Saoudien comes from the first 'king' who founded the country.