I have 2 that look like this one. One is called blue bell, and the other is Etoile Violette. Not for sure which one it is. My blue bell is in bloom right now.

Thanks. Someone else mentioned Etoile Violette too. I don't remember my other clematis blooming twice but then again I haven't paid much attention to them.
Karyn

I don't think Etoile Violette is one that commonly has a spring then fall flush of bloom. It is a Viticella and they usually bloom in summer.

How big are the blooms?

A lot of type 2's bloom twice and they have bigger blooms than the viticellas which are type 3's.