At the end of the first book, the Neanderthal has gone back to his world, leaving the rape victim who has come to love him on our world. In this book, he and an ambassador are sent back here and Sawyer spends almost the entire book telling us how much better the Neanderthals (as he sees them) are than we are. The ambassador brings the top 10 artisans and inventors to the UN and offers all their expertise to our world, the Neanderthal says how irrational we are (his suggestion that if all presidents had to announce war in front of the Vietnam Veterans Memorial, they wouldn't, is clearly wrong), and when the woman from our world goes to theirs, she finds it easier to work without men (the way their society is set up). The book does advance their relationship.
The third book (which is not here yet) had better be good.