I was born in the Netherlands from Dutch parents and still only hold my Dutch citizenship. I have lived in South Africa since 1955. Both our daughters have Dutch passports. Is it possible for my grandson to apply for Dutch citizenship (he is 18 years old)?
I assume that your grandson is the son of one of your daughters. I also assume that this daughter's Dutch passport is currently valid. Please advise if either of these assumptions is incorrect.
That your grandson's mother has a Dutch passport is only of limited use in answering the question of your grandson's nationality. What matters is that she has been a Dutch national at every moment between his birth and his 18th birthday. If she was, then he cannot apply for Dutch nationality because he is already a Dutch national.
If she lost her Dutch nationality before he turned 18, however, he also would have lost his Dutch nationality at that point. Presumably she did not lose her Dutch nationality before her last passport was issued, so the question is whether she has lost it since then. The last passport (if valid) can't be much older than 5 years, since the Netherlands switched from 5-year to 10-year passports about five and a half years ago. To be precise, her passport must have been issued on or after 9 March 2014.
The most likely way for her (and him) to have lost Dutch nationality would be her naturalizing in another country (e.g., South Africa). If she acquired South African nationality from birth, however, she obviously did not naturalize in South Africa after 9 March 2014.
Another possibility, depending on when your daughter was born, is that her passport was issued more than 10 years ago (in which case it is no longer valid, of course). If that is the case then she may have lost her Dutch nationality under the 10-year rule (or the slightly different 10-year rule that pertained from 1985 to 2003 or so).
Since it seems probable that your grandson is a Dutch national, he should apply for a Dutch passport. See Waar kan ik een paspoort of ID-kaart aanvragen als ik in het buitenland woon? (in Dutch) or Applying for a Dutch passport abroad.
Important note: As mentioned above, Dutch nationals who also have another nationality can lose Dutch nationality automatically in some circumstances under current law. If your grandson is a dual national and does not request a passport, ID, or consular declaration of Dutch nationality before his 28th birthday, he will lose is Dutch nationality. Your daughters may also have to worry about this.
Changes in the law are being debated, so it is a good idea to follow them in case the conditions leading to loss of Dutch nationality are changed.