Looking for name of author and title of books: story is a meteor hits
a cruise ship with a professor and young woman - they wake up on
another planet in the bodies of human-like creatures, who have
telepathic communication capabilities with very large cats. Read these
in the mid-80's in the US.

Dear margaux-ga,

From your description, I believe the book is, 

The Gandalara Cycle (1986), an omnibus of novels by Randall Garrett
and Vicki Ann Heydron.

The first book in the cycle is an omnibus edition of the first three
books in the Gandalara fantasy adventure series - The Steel of
Raithskar : Bantam, 1981; The Glass of Dyskornis  Bantam, 1982; The
Bronze of Eddarta : Bantam, 1983.

This is an extract from a review of the book,

"Title: The Gandalara Cycle I
Author: Randall Garrett and Vicki Ann Heydron

Ricardo Carillo, an aging language professor, is on a Mediterranean
cruise ship when it is hit by a meteor. He wakes up in a blinding hot
desert, sharing the body and some of the memories of a young man named
Markasett. Not quite human - supraorbital ridges around the eyes and
large canine teeth. The first being he encounters is a huge cat,
bigger than a horse, called a sha'um. The sha'um's name is Keeshah,
and recognizes Carillo as Markasett. Carillo discovers that the 2 of
them are linked telepathically, after being scared half to death."

(Text located near the bottom of the page)
http://www.webmoose.com/owc/fiction/rev-detail.php

The books are out of print, but seem to be available used.
For example:

amazon.co.uk for Cycle 1
http://www.amazon.co.uk/exec/obidos/ASIN/0553259423/qid=1079686890/sr=1-2/ref=sr_1_8_2/026-6051360-7526851

amazon.com for other books in the series
http://www.amazon.com/exec/obidos/search-handle-url/index%3Dbooks%26field-keywords%3Dgandalara%26store-name%3Dbooks/102-8330391-6696126

To find out more on the series, use the search term "Gandalara Cycle"
supplied below.

I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder

Search strategy
"cruise ship" meteor professor "sf"
://www.google.com/search?q=%22cruise+ship%22+meteor+professor+%22sf%22&hl=en&lr=&ie=UTF-8&oe=UTF-8
"Gandalara Cycle"
://www.google.com/search?q=%22Gandalara+Cycle%22&hl=en&lr=&ie=UTF-8&oe=UTF-8

Excellent! I can't believe how fast it was, and how complete the
answer! I've been looking for years!
Thanks.

Dear margaux-ga,
Thank you for the rating and the tip. Pleased I could help.
answerfinder-ga