Subject: Gender genetics and expression in sex-changing animals

I've read in the past about animals (fish, I believe) which change
their genders depending on age and environmental conditions.  If I
remember right, they're able to produce eggs while female, and sperm
while male.
How does this work?  I presume they have sex chromosomes, and are
therefore genetically one gender or the other.  Which?  Do they have 
both ovaries and testes, or do the ovaries turn into testes?  I 
understand how secondary sex traits can be altered, even in humans, 
by hormonal changes, but I'd thought that internal organs were pretty 
much set in stone during development.

Re: Gender genetics and expression in sex-changing animals