Okay, Scotty made his NWA/WCW TV debut at Chi-Town Rumble 89 in February of that year. They started teaming not too long thereafter.
Rick suffered an injury in the fall of 92 so Scott began a singles career and won the TV title from Steamboat. By late October they were both off of WCW TV and made their WWF debut at a TV taping in mid December 92.
They hung around in the WWF until about February of 94. When they didn't recieve the tag title shot at WrestleMania X, it was clear that they were on their way out. The brothers made one last appearance, after they had already started shows in Japan, when Scott met IRS in the KOTR Qualifying round. That was around April. After that, they were gone.
They showed up in ECW in 1995.
They made their WCW return in March 96 during an episode of Nitro as they took on the Road Warriors.
Their Japan schedule was sparadic. When they weren't in the big 3, they would be in Japan. Even when they were in NWA/WCW, they would have a pretty decent tour of Japan since they were multi-time holders of the IWGP tag titles.