Thunderfox - Finish first in Alpha Circuit
Mad Falcon - Finish first in Gamma Circuit
Stingray - Finish first in Delta Circuit
Piranha - Finish first in Epsilon Circuit
King Komet - Finish first in Omega Circuit

These licenses will give you the ability to drive in the next circuit and race in those tracks.

License Class "C" - Finish first in Alpha Circuit
License Class "B" - Finish first in Gamma Circuit
License Class "A" - Finish first in Delta Circuit
License Class "S" - Finish first in Epsilon Circuit