No, with "parents" you want a "have"; in both cases parents is the subject. And BTW, I'd add "one" in the second sentence: his parents haven't one either.
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EladioConsider these sentences. Some people around me think "have" is the only correct way. I think both are correct. Any help from you?: Bob hasn’t got a pool and neither have (HAS?) his parents. Bob hasn’t got a pool and his parents haven’t (HAS?) either. Thank you, Eladio