The 6 speed manual transmission in 1989-1996 Corvettes was produced by German automotive components company ZF Industries http://www.zf-group.de/. The Corvette Owners Manual clearly states that this transmission does not need service, but the transmission fluid level should only be checked and kept full. A bit of research confirmed that ZF does not share this recommendation with GM. Instead, ZF recommends that the transmission oil be changed every 30,000 miles.
The rear axels in C4 Corvettes are from Dana Corporation http://www.dana.com/ GM does not specify a service interval in the owners manual. Dana Corporation makes the following recommendations: 1. If there is any possibility of water contamination the oil needs to be changed immediately.