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My C5 (Coupe/auto) is 6 years old, has 15,000 miles, and gets driven about once a week. About a year ago I started noticing an occasional drop of clear thick fluid (the size of a penny following spreading on the garage floor) under the rear transmission/differential. I called a Chevy dealer and they want $1200 to replace all the gaskets, seals and o-rings in the rear end. Does this sound reasonable, and will it damage the car to drive it?
Sounds like gear oil. The most likely cause are the side axle output shaft seals. I know there is an updated part number, but I can't remember it off the top of my head. $1,200 seems pretty steep for this job. It won't hurt anything to drive with a minor leak, however I would check the diff gear oil level occasionally to make sure you're not getting too low.
It will not hurt to drive it as long as there is enough fluid in the diff.
$1200 seems stiff, but there is a fair amount of labor to the process, you need to remove the differential and then the side covers of the differential (that is if you are going to do all the o-rings AND the axle-shaft seals.....the shaft seals can be replaced with the differential in the car...)
If you are handy and have the facilities, you can save 80% (guesstimate) of that cost by doing it yourself or with a knowledgeable friend, buying the parts yourself.
If it is an axle shaft seal, or side cover, it is a pretty straight forward job. I replaced my drivers side axle seal and cover seal in about 6 hours using basic mechanic tools with the rear on jack stands. There is a TSB that GM put out that discusses the problem of leaking seals and there recommended fix. You can read it on the corvette action center website. I recommend you get under the car and identify the leak location. $1200 is a lot of money, but to replace all seals, the diff will have to come out of the car. There is also a good procedure on replacement of the axle seal on the forum, which you should be able to find by a search if you want to tackle the job yourself. Good luck.