Issue with recording 2 tracks simultaneously

I am trying to create 2 part harmonies in Audacity. I record the first track just fine, but when I record the second track, the only parts that are picked up on are the parts that have not been recorded in the first track. I know it sounds confusing, but it seems as if Audacity rerecords the original track while I am in the process of recording the second track, and all you hear is random bits and pieces of the second track when played together. Help!

Do you mean that the first track is being recorded onto the second track along with your new sounds?

Which version of Audacity?
What operating system?
What sort of microphone?
What sort of sound card?