What is the relationship like between David and Uncle Axel in The Chrysalids?  

David’s Uncle Axel is very supportive of him, and they have a father-son relationship that is much better than the one between David and his own father.

David is much closer with Axel than his own father.  He was married to one of David’s aunts who died.  He calls David “Davie” and never yells at him or beats him.  He just looks out for him and gives him advice.

He was a useful all-round man, though slow in getting about because of his leg, so my father let him live with us: he was also my best friend. (ch 2)

Uncle Axel is an unusual person.  He and David are close.  David describes him as his “best friend among the grown-ups” (ch 4).  Most of the people in Waknuk are strictly religious or just afraid.  Axel, on the other hand, is sensitive and caring.  He accepts differences and acknowledges change.  In this way, he is a good role model for David, because David has almost no one he can confide in about his special powers.

Uncle Axel discovers David’s telepathy by accident, when David is talking to Rosalind one day using words—and she is nowhere around.  He warns David to be careful, because if he is shown to be a deviant his certificate of humanness will be revoked and he will be expelled.

I want you to promise that you will never, never tell anyone else what you have just told me -- never. It's very important: later on you'll understand better how important it is. You mustn't do anything that would even let anyone guess about it. (ch 4)

Uncle Axel stands up for David and the other telepaths from that day on.  He helps David discover why one of the telepaths was missing (he was killed in an accident), and he realizes that Petra is also capable of thinking in thought-pictures, even if she is too young to understand what it means.

Uncle Axel is there for them when Anne tells her husband she is telepathic, and he kills the man before he can betray them.  He is willing to do whatever must be done in order to make sure that David and the others are safe.

Axel’s presence in the story is important.  He demonstrates that not all people in Waknuk are so highly religious and intractable.  He shows the kind of evolution of thinking that the Sealanders support.  He also gives David a refuge in a difficult world, making it easier for him to face his challenges.