The allegation for one of the cases is approximately this: they were going to have consensual sex, but the girl required that he wear a condom. One was not available, and so she refused to allow sex. They stayed in bed together, and fell asleep.

In the morning, she woke up to Assange on top of her having sex with her. She asked if he had obtained a condom and he said no. She told him to get off, and, well, he got off, but not in the way she meant--he kept going, came, and then withdrew.

That would arguably be rape in the US.