An automatic transmission fluid leak may develop from the rubber section of a transmission cooler line. In some cases the rubber section of hose can be replaced. In others, the complete cooler line must be replaced to correct this type of leak.
Car problem reports
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Most reported 1996 Buick Riviera problems
The intake manifold gasket may develop external engine oil leak. The manifold gasket will need to be replaced to correct this issue.
The fuel pump may fail causing the engine to stall and not restart.
The air conditioning system can be prone to refrigerant leaks and failure of one or more pressure sensors. The AC pressure sensors should be checked for proper operation when ever the AC system is serviced.
The front struts may show signs of wear, or be excessively bouncy ride at freeway speeds. This may begin to occur at around 75,000 miles.