United States 
Do you remove the dead flowers?
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clematis plants page
31 May, 2010
Answers
Depends on the variety - C. tangutica, for instance, is grown as much for its decorative, fluffy seedheads as it is for its flowers.
1 Jun, 2010
Previous question
I would, if only for neatness. Some varieties will try to produce seed, which will take energy from the vine, and future flowers.
1 Jun, 2010