There were at least two bands that have recorded under the name The Impossibles. They are, chronologically:

1) a well known thai funk/pop band active in the 1970s.
2) an alternative/ska band from Austin, Texas
1) The Impossibles (Thailand) composed their own hits but were also known for their covers of Western rock songs. They were among the first Thai pop bands to cover English language songs and were the first Thai rock band to record an English language album overseas during a tour of Europe.

Read more about The Impossibles on Last.fm.