Ayeka is the first princess of Jurai. She is also one of the many girls that has feelings toward Tenchi. Princess Ayeka has decided to stay with Tenchi along with her sister Sasami.
Ayeka sometimes may act like a spoiled brat, but that is the she was brought up. As a princess, she probably has never worked to get what she wants, but in Tenchi's case, she'll make an exception. She always seems like she wants to tell Tenchi something, but can't find the right words. She puts her responsiblities first and her needs second.