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I put new Firestones runflats on the back and kept the Goodyear runflats on the front because they still had a lot of tread left---and I haven't had any problems whatsoever. On the other hand, I don't do a lot of aggressive driving so it probably isn't as noticeable. I will, however, be putting new FS on the front in about a month. Given the choice, I would run the same tires on all four corners.
:nono: :nono: :nono: Just remember the two most important factors regarding your well-being (staying alive) as a vehicle operator - good tires and brakes. These are two areas where you never want to be frugal. I wouldn't mix tire brands on my Jeep let alone the Vette. If you need more convincing, just go the http://www.tirerack.com website and see for yourself. :smash:
I wouldn't foresee a stability issue, but the overall effect would depend on what tires were on the rear. The Goodyear runflats have very still sidewalls and as a result are not very compliant, which seems to be a bigger problem on the rear than the front of a C5. If I were to assume that you would be running a non-runflat on the rear, chances are they would be more compliant and likely stick a little better than the fronts. The result of this would be that the car would tend to understeer a little more than before (more traction in back relative to the front). This is a very safe condition.