There is no problem with the tenses, but I don't know what you are trying to signify by "yet". " At the same time as he stood up, he was holding the book firmly. "whilst" is chiefly BrE.
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AnonymousThanks for your response. I thought words like 'yet' or 'still' would add more emphasis to the fact that he was still holding the book (while performing another action).I see, yes, "yet" can be used in this kind of way, but it sounds literary or old-fashioned, and I wouldn't particularly recommend it.
Anonymous"whilst" is a contraction for "while still."No, it isn't. http://www.etymonline.com/index.php?term=whilst