Tires: Different tires on the front and rear., goodyear eagle f1, michelin pilot sport

Question
I want to put new 17-inch tires on a 1987 Buick Grand National, with wider ones on the rear. I can only do this and get quality Max Summer Performance tires by mixing brands; putting 235/50-17 Michelin Pilot Sport PS2 tires on the front and 255/45-17 Goodyear Eagle F1 GS-D3 tires on the rear. This configuration would be on the car for a long time, as it is only driven about 500 miles per year. Would I run into any problems by using two different brands and tread patterns for this application?

Answer
Rick,

Obviously the best situation is to have 4 of the same tire on the car.  

Having a mix of tires on a car is problematic as it can cause an imbalance in the way the car handles.  There's no way of predicting what combinations will work - and which won't.  But the worst of this is that this imbalance usually only displays itself in emergency hanlding manuevers - just when you'd want the vehicle to behave predictably.