What evidence is there that his feelings for her are genuine?
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The evidence that the Commander does have genuine feelings for Offred can be found in the fact that he allows her to break the rules at his own risk. If she were just someone he used for sexual gratification it would be easy enough to send her away, but he doesn't. He gives her as much as he can without revealing anything outside of the room they share when they're together.
The Handmaid's Tale/ Chapter 29