The band's big hit was their 1984 single "Heaven (Must Be There)," off their second LP, This Island. I'm not sure how much airplay the song had on radio, but the video was in rotation on MTV for a time. In any event, "Heaven" peaked at #65 in the U.S., while the album stalled at #140. In contrast, our Australian reader(s) may recall that the song reached #2 on the charts there (the album hit #4), one of seven top 40 hits in their homeland.
Eurogliders broke up in 1989. Lead singer Grace Knight went on to have a successful career as a jazz singer and several of the other members remained in the music industry. The band has sporadically re-formed since 2005.